3 to the x = 20, many don’t know where to start

An introduction to solving exponential equations using logarithms.
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[@jetman551]

Armstrong and Aldrin carried a Pickett slide rule to the moon as a backup.

[@douglasfaloon5340]

I’m 80 and love this algebra refresher . Thanks,

[@charmer1979]

Did you have a log book at school, I can remember my dad having a little log book with tables in it. Ps never too old to learn, I'm 53 and I've just started a maths degree.

[@danielrankin857]

Too much too late...50 years too late...I sure could have used your tutoring then! Yet...I'm never too old to enjoy math thanks to you. Bless you!

[@lynnyrouse8192]

Never too late to learn. I'm 62.7 yrs old and most willing to learn. It helps your cognitive development which decreases as you slow down in age. Don't do that.

[@Jim-fe2xz]

I graduated college in 1970. We use slide rules and tables. In the early 70's my best friend gave his a dad a special gift of a "Bomar Brain" calculator. It multiply, divide, add and subtract LOL! Now my iphone does everything I need to follow along with your videos! I appreciate an enjoy all of your efforts! I wish I had you as my math teacher in the 60's!

[@pieterlabuschagne7507]

I enjoy this basics. Keep up the good work John. At school we still used log books in the 70ties

[@charlesgarnier4255]

When I attended the royal military college in 1973, we were issued a slide rule. A bunch of the first years ordered Texas t1 calculators after Christmas. I couldn't afford the cost so bought a calculator from sears in the summer for about 100 dollars that gave me four functions and percent.

[@wmfield152]

There's a lot here in just a few minutes. This was an excellent explanation of logs & exponents.

[@Nikioko]

17:44: You wouldn't look up log20 in a logarithmic table. At least, you wouldn't find it. What you find is lg(2) = 0,3010. For lg(20), you have to add 1 to get 1,3010.

[@martinfiedler4317]

Worked this out with my slide rule. Surprisingly accurate: 2.73

[@johnplong3644]

When I graduated High School in 1976 Texas Instruments had Calculators for about $150 Maths students were Already using them In Trig and pre-calculus In Algebra 2 we had tables in the back of the book I do remember High School math students using slid rules in 1972 in my Freshman year of High School I never learned to use a slide rule.

[@russelllomando8460]

I didn't think slide rules existed anymore. Nice job.

[@martinfiedler4317]

​@@russelllomando8460 They aren't in production anymore. Bought a used one in excellent conditions. Wonderful thing! And can always double as a regular ruler 🙃

[@devonwilson5776]

Greetings. The answer is determined by taking the Logarithm of both sides. That is 3^X =20 and Log3^X = Log20. Moving on, X Log 3 = Log 20 and X = Log 20/Log 3 = 2 . 73 rounded.

[@kurtmooreca]

how did you calculate Log?

[@TPJ79]

use the log button on your calculator and divide log 20 by log3

[@Nikioko]

12:00: Even if it doesn't matter, but each logarithm goes with a base, which is missing here. Of course, there are the special logarithms ln, lg and lb with the bases e, 10 and 2, respectively. But any logarithm with “log” needs a base specified.

[@alext8828]

No base indicated means base 10?. I think I remember that. The other two are labeled as such? Good point.

[@kurtmooreca]

1 sec guess. First step Identifying the limits. 3^3 is to big, and 3^2 small. So it must be some where in between but closer to 3 and further from 2. (thanks to 3's relationship to 21 the next integer, where 2 doesn't have one that is whole number) There are now two steps we must process, for each iteration of 3 multiplying into itself at least twice, with a partial third. 1. 3/2 = 1.5 + 1 (place holder for the next 3 as an exponent) = 2.5 2. 3/2.5= 1.2 + 1.5 (place holder for 3 as an exponent from step 1 minus one 3 because its step 2 or 2.5-1 =1.5, and now being represented by 1.2). = 2.7 Now we have identified that 3^x = 20 must be some fraction or decimal rate of 2+.7?????. From this point we use some "abstract" but basic math to identify the decimals, which is pretty easy as its pretty basic multiplication but can be confusing as we are are looking for 2 numbers that both don't go over the defined .7 we have established, but also break down into 20 and 200 (tenths and hundredths) working "backwards" from the decimal positon. First number. (adding in the tenths, so measuring to 20 without going over the defined 7 for rounding reasons) 2x2 = 4 2x2x2 = 8 This says that .73 is to high and that .72 is in the ballpark. Second number (adding in the hundredths so measuring to 200 again without going over 7) 2x2 = 4 2x2x2=8 2x2x2x2 = 16 2x2x2x2x2= 32 2x2x2x2x2x2=64 2x2x2x2x2x2x2=128 count up your 2s and you are done. 3^x = 20....x = 2.727. or 3^of 2727/1000 = 20. And check, 3^2.727 = 20.003669, = 20.004, and thats as close as you gonna get because 4 ain't rounding itself up to an irrelevant .01 any time soon. And now to enjoy the video (love this channel btw) Edit: also you don't need a calculator, for this, just need to be able to place hold in your head or on paper. This is solvable by % based math and knowledge of fractions, and of course knowledge that the right side of a decimal works inverse to the left side, but follows the same rules.

[@carlmarch603]

It’s 2.73 if rounded, not 2.72, since it’s 2.72683. That said, as an old retired scientist, I enjoy your channel and have used it to help my grandchildren. Thanks!

[@kurtmooreca]

The answer to 3 decimal places is 2.727, 2.73 = 20.0697 which may as well be 20.1 when rounding. 2.727 = 20.0036, or 20.004 if you want to round. Feel free to type it into your calculator if you don't believe me, 3^2.727 is much closer to 20.0 than 3^2.73 is, and .004 can't be rounded up thus equating to 20.000 when its rounded down.

[@russelllomando8460]

I originally learned to calculate logs manually. How times have changed in 55 years...

[@johnplong3644]

Same here

[@argonwheatbelly637]

Table of Logs, man. That's the way.

[@russelllomando8460]

I don't do calculators, I like the brain workout. I got it to approx 2.75 (mentally) I'm happy with that outcome. Thanks for the challenge.

[@olivemd]

Ditto.

[@kurtmooreca]

pretty darn close, the answer derives at 3 decimal places 2.727, which result in 20.0036 about as close as you can get with head math. 2.75 is a bit higher resulting in rounding termination of 21, but you were right in the ball park. I explained the process in another comment on how to break down Logarithmic equations...if you a math fan you should check it out.

[@sharongrant789]

Great reminder...thank you..I will be a forever fan.

[@heli4630]

I am almost 85 and many moons ago I made the Abitur in Germany completing the necessary math curriculum required for that course of study. I hated it with a passion. Now I find it challenging and interesting thanks to your efforts. Keep it up ! Maybe the few ‘math geniuses’ who leave nasty comments, could stifle themselves and not spoil it for us other folks. I find them irritating.

[@panzerabwerkanone]

I nearly forgot logarithms. This brings back the nightmares. Thirty years of therapy down the drain.

[@laurendoe168]

After describing "bacon and eggs", it should be obvious that x= log base 3 of 20. So what exactly IS log base 3 of 20? You say the answer here is approximately 2.72, but here is why I believe converting logs to decimals is quite limited: I have a calculator that does "x to the power y". When I type in "3 to the power 2.72", the answer is 19.85. (my calculator says log 20/log 3 is 2.7268330278608420413960946363642... which should be approximated as 2.73 (or 2.727))

[@kurtmooreca]

you can just learn how to do Log though and not need a calculator at all. I derived the same 2.727 just using math in a comment above. I mean we had to have known how to do Log before we programed calculators to do it for us.

[@laurendoe168]

@@kurtmooreca Yes, there were logarithm tables printed on scores of pages, and I believe slide rules had a log scale if you didn't need too much accuracy.

[@mrapp10143]

I remember those tables in the back. But I guessed 2.66 after realizing it had to be between 9 and 27. Then I figured it had to be approximately 2/3 of the way. So close. And yes, when I gif to college, they required that expensive scientific calculator (about $200 for that Texas Instrument one)

[@user-qk9tq1rt7o]

3 Exponet X = 20 is the same as cubed root of 20 is it not?

[@terry_willis]

Looks to be Yes. 2.72^3 = 20.xx

[@larryrichards3668]

It's close. cube root 20 = 2.714 The log 20/log 3 = 2.726

[@pmw3839]

The log of a number (in this case 3) = the number converted into the exponent of 10. This is like converting it into a different language. An exponent raised to a power (in this case x) = the exponent multiplied by the power. The other side of the equation (20) must also be converted to the same language.

[@ChiragSonne]

I watched your video on yesterday evening @TabletClass Math😁

[@justmeonly986]

L O V E this! I'm a "back of the textbook" person. My brother was a slide rule genius.😊

[@colleenjeffries3334]

I love algebra!

[@bobcornwell403]

I got approximately 2.73 for the power of 3 to equal 20.

[@mike-yp1uk]

That was awesome

[@billbrownster]

I still have my Pickett slide rule. 1960s manual math calculator.

[@srdjannalis3037]

You spent 20 min to show how to solve this simple task. It could be solved in a two seconds. Only you must see values for log because nobody know values of logs.

[@syedmdabid7191]

Xlo3= 2 log2 + 1--log 2 , x= 1+ log 2/ log3 responsi.( 1+ log 2) /log3

[@paulregret3180]

You are knowledgeable. Try to cut you explanations in half to improve your channel

[@betqpublic9901]

Slide rules mad me math phobic I knew how to do it but kept getting the wrong answer. Teachers couldn’t figure out what my problem was. Years later I discovered I had an astigmatism so I was always off by a couple of degrees which in turn made me get it wrong Still hate them even with a calculator

[@Jlalode]

OMG! I remember those log tables 🤪

[@felixbrandt6419]

The next digit behind this second 2 in the result is a 6. So it is 2.73 rounded, not 2.72.

[@fosterdyche]

Hmmm 2.73 using proper 5/4 rounding rule.

[@stevenscottoddballz]

I never understood: why is the button marked [LN], when it is called "Natural Log"? Shouldn't the button be marked [NL]?

[@felixbrandt6419]

Sometimes it is called "Logarithmus naturalis". That is why. I guess this is some sort of Latin.

[@marywilkins6244]

Solution starts at 12:15

[@pmw3839]

Very helpful. Thank you.

[@JekKent-xb3lf]

Exactly too much waffle which confuses the solution imho

[@davidlemieux398]

2 to the 4th power is written 2x2x2x2. How would you write 3 to the 2.7 power?

[@ndailorw5079]

@davidlemieux398 To the best of my knowledge and understanding, there’s no way to represent bases raised to a fractional power in similar notation like bases that are raised to whole number powers, such as, a^4 = a • a • a • a, 4 being a whole number. 2.7 is a fractional power. An improper fraction, to be exact, written as, 2(7/10) = 27/10. So that 3 to the 2.7 power would be written as, 3^(27/10). Which is the same thing as taking the 10th root of 3 raised to the 27th power. The answer is approximately 19.41, which is close to 3 raised to the 3rd power, or, 3^3, which equals 27. If you’ll notice, for example, the square root of 16 is a base also raised to a fractional power, it’s not raised to a whole number power. When written in fractional notation it becomes (I don’t actually know if there’s a name or term, or what we should call it, I’m just calling it “fractional notation”), 16^(1/2) or 16^(0.5) or 16^(5/10), which reduces to 16^(1/2). Which is the square root of 16 raised to the power of one, 1 being the whole number, or, in other words, the square root of 16 raised to the first (1st) power. It can’t be simply written like, say, the expression a^2 = a • a, which a base raised to a whole number power, (a) being the base, and 2 being the whole number. Notice also that taking radicals, that is, taking roots of bases is the inverse process of raising bases to some whole number power, and vice versa. For example, taking the square root of 9 is the same thing as “raising” 9 to the one half power (9^(1/2)) and as such is the inverse process of raising 3 to the second (2nd) power, which, the inverse of raising 3 to the 2nd power (3^2), which is 9, is taking the square root of 9 (9^(1/2), which is 3, and vice versa. In other words, one can be used to solve the other, reciprocally. So that bases raised to a fractional power are in essence and effect the nth root of that base raised to some whole number power, like so, a^(x/n), n being the denominator and the root, and x being the numerator and the power of the fraction, or “fractional power” (x/n), and the base, (a), being the base raised to that fractional power. Just bear in mind, that, when some base is raised to some “fractional power,” “we’re doing radicals, we’re taking roots,” at that point, “we’re doing roots”! So if I see 5 raised to the power of 0.75 or to the 3/4 power, raised to a “fractional power,” 5^(3/4), or 5^(0.75), I know immediately that I have to do the inverse of raising the base to the whole number power and instead do the inverse process and take the 4th root of the base 5 raised to the 3rd power; I know immediately that I’m dealing with a radical (root) and have to take the 4th root of the base 5 raised to whole number power 3, the inverse of raising bases to whole number powers. So… when I see 3 raised to the 2.7 power, or 3 to the power of 2.7, (which is 27/10, more simply), I immediately know that I must take the 10th root, which is the denominator, of 3, which is the base, raised to the 27th power, which is the numerator! Hope that helps and doesn’t confuse things. Heck, hope that’s correct….

[@clydebennish2106]

I worked this out with my slide rule but verified the answer with a calculator (I cheated). Im still a bit rusty on logarithms. X = Log 20 / Log 3 = 2.73 or X = Log Log 20 - Log Log 3 = .436 which is the Log of 2.73 My first time ever using Log Log... Took me a while.

[@user-ri6rn7ti5h]

(x+8x-3) (x+2x-5)

[@danieldennis9831]

x≈2.7268 (ln20/ln3)

[@alext8828]

Can't this be interpolated somehow? It seems to me that we used to do that back in the early '60s. I was very bad at it.

[@user-yh7cl9kj8k]

Just get on with it!!!!

[@o-1111]

Actually the solution started at 12th minute in a 20 min video. . Total waste of time

[@giannaleoci2328]

log3^x=log20 xlog 3=log20 x=log20/log3

[@ozfire7]

2.726

[@dchall8]

Omuhgoooh! Why does it take sooo long to get to the point?

[@Karen_DNP]

3^x = 20 x = 20/3 Log 3^x = Log 20 x = ~2.72

[@thomassicard3733]

Aprox. equal to 2.73

[@bobpollack6894]

2.7 on paper

[@RockyS1945]

age 79 and still counting-how vague.

[@user-ri6rn7ti5h]

62740

[@colleenjeffries3334]

This can be solved without a calculator.

[@thomaswinston5142]

2.73 is closer

[@oldschoollew]

the title is apropro are you loking for a number.... and the answer was yes

[@slomo1716]

why can't the answer be 3 power of (3 minus 7) ?? so 3x3=9x3=27 - so minus out the 7?? This is the first video I've watched where you actually show us how to calculate the answer of how to translate numbers with powers. Why does this have to be so stinking difficult - log? bacon and eggs?? NUTS TO ME!! very fanciful way to find an answer which still doesn't make sense!

[@brianmurphy4702]

log

[@Dbaby52]

Xlog3base3=log20base3 x=log 20base3

[@ayushchoudhary4842]

Simple bro use log

[@harrymatabal8448]

We dont know whete to start because we are stupid

[@m.h.6470]

Solution: 3ˣ = 20 |log log(3ˣ) = log(20) x * log(3) = log(2 * 2 * 5) |:log(3) x = (log(2) + log(2) + log(5))/log(3) x = (2log2 + log5)/log3 x ≅ 2.73 alternatively, you can work with log base 3: 3ˣ = 20 |log₃ log₃(3ˣ) = log₃(20) x * log₃(3) = log₃(2 * 2 * 5) x * 1 = log₃(2) + log₃(2) + log₃(5) x = 2log₃2 + log₃5 x ≅ 2.73

[@stevewthespider]

Bad rounding, should be 2.73

[@argonwheatbelly637]

"MANY DON'T KNOW WHERE TO START" --

[@robinbjerregaard4077]

How do you use 20 minutes explaining exactly nothing? WTF does the bacon and eggs segment have to do with the solution? Saying "if you've studied logs long enough you know they have magical properties like moving this x" in MULTIPLE videos IS NOT AN EXPLANATION. YOU literally don't actually understand yourself, DO YOU? THOSE OF US THAT DO CAN TELL

[@timesfire]

So, after twenty minutes of babbling and drawing with your little light pen, the answer is “use your calculator”? What an utter waste of time.

[@heatherbartusch5239]

Mr Math Man...thank you for your videos. Yes I'm one of the grey matharoos, 🦘, coming back to study. You have helped sooooooo much. Keep it simple and direct. Love your videos. Again, thank you😊❤🎉