4 to the (3x - 6) = 64, you can solve with BASIC MATH!

[@robertstuart6645]

Nice to see problems of this kind. I never recall seeing them in all of the math classes I had.

[@devonwilson5776]

Greetings. The answer is 3. 4^3X-6=64 is 4^3X-6=4^3. Since the bases are equal, the exponents are also equal. That is 3X-6=3, 3X=9, adding 6 to both sides of the expression, and 3X/3=9/3, dividing each sides by 3 gives X=3.

[@johnmarchington3146]

When you discussed the logarithmic approach and you had log64, you could have mentioned that that would be equal to log4³ - and thus 3log4 - and as that was being divided by log4, the answer would have been 3. Another excellent video. Thanks again.

[@chouchfroukh]

Log 64/ log 4 = log 4^3/ log 4 = 3log 4/log 4 = 3. Without calcuator.

[@mercy3648]

1. We have the equation: 4^(3x - 6) = 64. 2. Notice that we can rewrite 4 and 64 has powers of 2; so we have: (2^2)^(3x - 6) = 2^6. 3. Now, we’ll use the rule, which says that if x^m = x^n, then m = n; so we now have a basic equation: 2(3x - 6) = 6. 4. Now we distribute the 2, so we have: 6x - 12 = 6. 5. Now we move the 12 to the other side: 6x = 18. 6. Finally, we divide the equation by 6: x = 3. Final ans: x = 3. Ez

[@laurendoe168]

Even easier - 64 is 4 cubed.

[@mercy3648]

@@laurendoe168you’re right. But I love math and believe it or not, I don’t like “shortcuts”. I enjoy doing math the “hard way”, you know?

[@laurendoe168]

@@mercy3648 LOL :D I must admit that the first thing I thought of when I saw the problem was using a common base of 2... until I noticed that a common base of 4 could also be used.

[@Kleermaker1000]

Only two fundamentally different ways: 1) 3 X - 6 = 3 etc. and 2) the logarithmic method.

[@tomtke7351]

Inspection suggests 4^3=64 Might we conclude 3x-6=3 3x=9 x=3 VERIFY 4^(3X-6)=64 with x = 3? 4^((3×3)-6)=?64 4^(9-6)=?64 4^3=?64 64=❤64✔️

[@chrisdissanayake6979]

4^3x-6 = 64 64= 4^3 4^3x-6 = 4^3 3x-6 = 3 3x = 3+6 3x = 9 x = 9 divided by 3 x = 3

[@richardl6751]

In this case Log(base 10) or Ln can be used.

[@Ayelmar]

Solved in my head at the thumbnail, the answer is x=3. Here's the process I used to get that answer: First, we figure out what power of 4 = 64. 4^1 = 4; 4^2 = 16, and so 4^3 = 64. Therefore, 3x - 6 has to equal 3. Using basic algebra, we get: 3x - 6 = 3 Subtract (-6) from both sides: 3x = 9 Divide both sides by the coefficient, 3: x = 3. And so 4^3 = 64. (And it basically gets back to powers of 2 by a roundabout path....😉 )

[@stevenjohnson1143]

Knowing 4^3 =64 so the final exponent must be 3 if 3x-6=3 then adding 6 to both sides get 3x=9 finishing by dividing 3 x°3

[@thomasharding1838]

4^(3x-6) = 64 and 64 = 4^(3) => 4^(3x-6) = 4^(3) => 3x-6 = 3 => 3x = 9 => x=3

[@russelllomando8460]

got it 3 64 = 4^3 so equal bases (4) have equal exponents. 3X - 6 = 3 Solve and X = 3 simple. thanks for the fun

[@stevenjohnson1143]

I was tempted to use logs but took my final approach it was easier

[@chouchfroukh]

Good video

[@HirschElla]

3 4^3 = 64 deci 3x - 6 = 3 prin umare x= 3. (9-6=3)

[@TheAZZA0990]

Very simple - x = 3!! :)

[@johnmarchington3146]

4 to the power of 3 is equal to 64 so 3x - 6 - 3, leading to x = 3

[@jald910]

4^3 is 64 so 3x-6=3, 3x=9, x=3

[@larrystuder6378]

Yup, that's how I did it. All in my head.

[@craigsaunders7037]

3.

[@p.patterson2123]

3

[@bazkeen]

3. 4^3 = 64 so 3x3 =9 9-6 = 3

[@bravikumar8950]

👍👍

[@johnmarchington3146]

Sorry, my typo. It was supposed to 3x - 6 = 3

[@mylittlepitbull3143]

Easy problem. 5 seconds in my head. I'm still a genius.

[@dannyr403]

I read it as (4^3) * x - 6 = 64 and I came up with x = 1.09375 I guess I'm not as think as I smart I am.

[@robortoalmeida5331]

X= 3.

[@shakirhamoodi5009]

X = 3

[@pas6295]

No sorry 3xis 6+3. So xis 3

[@pas6295]

Xis 6

[@theperson4yearsago565]

Silly

[@samswift4921]

3

[@rajalakshmik6148]

X=3

[@josephlaura7387]

X=3

[@philipagbati]

X=3

[@rajeshvyas934]

X=3

[@RRRSSS1111]

X=3

[@kco513]

x=3