Lesson 3 Logarithms, Solving Logarithmic and Exponential Equations

Log Lesson 3
This video uses the laws and rules from lesson 1 and lesson 2.
5 exponential and 4 logarithmic equations are solved using log and natural logs.
Real life situation word problem is included also.

[@niceplayer856]

From India but also watch your videos just because of your amazing teaching style🔥🔥

[@mrhtutoring]

Awesome! Thank you!

[@user-ky5dy5hl4d]

@@mrhtutoring At 15:37 natural log of e on the right hand side is 1. That gives us 1 stil raised to power of -2t. One raised to power of -1 is 1. But what happens to t? And is 1 to the power of -2t negative 2t? Or should it be just t or -t? Let's say we have ln e to the power of 5x. So, ln e is 1 and we are left with 1 to the power of 5x. Do we multiply 5x by 1 or do we raise 1 to the power of 5x because 5x stil stays in the place of the exponent and 1 is the base. And it looks like you multipled one by -2t. Unconfuse me.

[@trevorjames4619]

Meanwhile, some student is paying an arrogant professor $10,000 a semester

[@citizenworld8464]

Once more, you render math simple and exciting. Again, thank you so much for sharing your knowledge, Mr H!

[@bellemiscellaneous9417]

Thank you for your videos! Very easy to understand!

[@cristianlezama5564]

Your videos and the time you take to make them are truly appreciated. Thank You very much!

[@iwjrbf99]

we would like to see u solving calculus problems, huge support from hong kong😻😻

[@HalifaxHercules]

I took some differential calculus courses when I was a Business student at Saint Mary's University in Halifax, Canada during the mid 1990s. While I'm familiar with limits, derivatives, and integrals, I would like to see some optimization and Law of Diminishing returns type questions.

[@devonwilson5776]

Greetings. Thanks always for sharing. Have a great day

[@alphasaffi9230]

Thank you very much sir may God richly blessed you for the time you take to impact knowledge in our lives.

[@amramjose]

Nicely done, professor.

[@HumphreyVV]

Hallo Mr H Tutoring, I am 80 years, and had the need to "brush off" some dust on past knowledge of your Topic. Well, after your video lessons, again ...I am on top of the subject. You have a marvellous way of making things look easy. Today is Christmas dec 26 in Holland, Merry Christmas to you, THANK YOU, and continue making things "look easy".

[@mrhtutoring]

Thank you. Merry Christmas!

[@castiodette]

Damn! I wish you were my teacher in math when I was in school. I would have been more attentive! Lol. You make math so easy! Thank you sir!

[@BWhiteHat]

First, also again, love these videos

[@andresomarlegarda616]

Gracias profesor, excelente, las matematicas el lenguaje universal.

[@emailinbox3260]

You are the best. Gracias

[@user-hx8dq9zn5z]

Good work Sir

[@merc340sr]

this video is AMAZING!

[@drask1717]

You're the best

[@BruceLee-io9by]

Dear professor, a big greeting from Italy. Thanks for your lessons.

[@Paulancar]

The best!!

[@alphasaffi9230]

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[@mrhtutoring]

You are very welcome

[@baselinesweb]

Thank you for the great review.

[@Nothingx303]

😊 thank you sir very useful questions 👍

[@88kgs]

Thank you so much sir. Regards🙏

[@user-hx8dq9zn5z]

I can recommend You an other channel for math Olympiad preparation

[@lawrencelawsen6824]

I love this guy

[@newme8084]

Thank you ❤

[@balukuchrispus4004]

My teachers were hardening math. Made easy here, waiting for integration, differentiation and flow chart

[@haroldjosephcollinsIII]

When the Bass meets the Treble i listen. When i Beat is about the nature of the Record i say "Turn it up!" I'd like to say something when i listen to a Record i am listening with an Ear to say i like it or i hate it. I don't minding thinking for you about this Lesson, but i am about the Record. I am the Owner of a Peer, but i am the CEO of Shore Entertainment Incorporated a California Corporation. ~ CEO this Record.

[@terrypold]

In skydiving you have to account for air resistance. So, assuming that the skydiver is falling in a vacuum the calculations are correct. And, the skydiver is dead.

[@thethinkinggamer1864]

Hello sir, you're method of teaching is extremely helpful, concise and clear, I'm from Canada and I'm wondering, which grade I will be using logs? Since I've just reached grade 11 and I've started quadratics.

[@mrhtutoring]

Usually in the 9th or 10th grade in the US

[@henna-designs-and-paint2268]

We learned logs in grade 12 pre-calculus classes in Canada. I hope it helps

[@apolloapollo3248]

❤❤ beyond

[@ART7N23]

Sir can u do teach vector basic ( short video )

[@ankitnauriyal6214]

Sir please explain under the root when can we cancel the root and when we can can't please sir make a vedio 💖

[@moeberry8226]

Good video bro but I want to point out that exponential equations can have imaginary solutions if you consider x to be a complex number. For example e^x=-2 has a complex solution.

[@mrhtutoring]

x=ln(-2)? The equation you gave has no solution.

[@moeberry8226]

@@mrhtutoring the equation I gave does have a solution x=ln(-2) can be broken into ln(-1)+ln(2)=ln(e^(ipi))+ln(2)=ipi+ln(2) as the principal root, this equation has infinitely many complex solutions. In general the solution is (2n+1)ipi +ln(2) where n is any integer and i is the sqrt (-1) so in our base case when n=0 we get the solution I stated 2 sentences back.

[@farhanfouadacca]

Nice

[@mayankshirali1158]

can you make a video about binomial theorem?? pleaseeee

[@mrhtutoring]

Will do soon

[@mayankshirali1158]

@@mrhtutoring thank you sir

[@charlieibkiss4068]

Good shit professor I love it!

[@josephveedock7815]

Barbarian at the gate

[@ChavoMysterio]

log_2(3)+log_2(x)=log_2(5)+log_2(x-2) log_2(3x)=log_2[5(x-2)] 3x=5(x-2) 3x=5x-10 3x-5x=-10 -2x=-10 x=5 ❤

[@ChavoMysterio]

3^(x+2)=7 x+2=log_3(7) x=-2+log_3(7) ❤

[@ChavoMysterio]

e^(2x+1)=200 2x+1=ln(200) 2x=ln(200)-1 x=[ln(200)-1]/2 ❤

[@drewbanares3577]

@10:52 Isn't something raised to the -x just the same as 1/x?

[@carultch]

No. x^(-1) is the same as 1/x. Negative exponents imply reciprocals in general, where the negative exponent becomes a positive exponent, once you move the power term downstairs. However, if x is in the exponent, instead of the base, it must remain in an exponent in some form or another. B^(-x) is not the same thing as 1/x of B/x, or anything else that only has x in the denominator. It is 1/B^x.

[@silent99gamer]

This is eassy

[@jmich7]

We are sure we can use the law of exponents, for the number was elevated to an exponent, right? There are many numbers; that elevated to an exponent allow us to use the log law of exponents. What numbers do not allow us to do so? Would we have to invent such numbers? To begin with all the numbers minus times a positive integer . We cannot take the log of a negative number...Let us start by saying that the log of a negative number is undefined........Or assuming the log of a negative number is undefined........

[@ChavoMysterio]

log(x+2)+log(x-1)=1 log[(x+2)(x-1)]=1 (x+2)(x-1)=10 x^2+x-2=10 x^2+x-12=0 (x+4)(x-3)=0 x+4=0 x=-4 (x[>=]-2; x[>=]1) extraneous solution x-3=0 x=3 ❤

[@robertjohnson1962]

If math were jazz, you’d be Miles Davis.

[@ChavoMysterio]

log_5(x+1)-log_5(x-1)=2 log_5[(x+1)/(x-1)]=2 (x+1)/(x-1)=25 x+1=25(x-1) x+1=25x-25 x-25x=-1-25 -24x=-26 x=13/12 ❤

[@ChavoMysterio]

4+3[log(2x)]=16 3[log(2x)]=12 log(2x)=4 10^[log(2x)]=10^4 2x=10000 x=5000 ❤

[@ashu4315]

Lesson is nice sir but try to include some tough questions

[@user-fq1wj8xj2k]

3^(X+2) = 3^X * 3^2 = 9*3^X 3^X = 7/9 X= ln(7/9) / ln3 = (ln7-ln9)/ ln3 = ln7/ln3 - 2

[@ChavoMysterio]

e^2x-e^x-6=0 (e^x)^2-e^x-6=0 (e^x+2)(e^x-3)=0 e^x+2=0 e^x=-2 (x>0) e^x-3=0 e^x=3 x=ln(3) ❤

[@haroldjosephcollinsIII]

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[@abijahmarshal]

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[@gamer0-0girl]

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[@user-fb6fl7zy6j]

Söylediklerinizi anlamıyorum ve buna gerek de yok çünkü yazdıklarınızı anlıyorum matematiğin dili evrensel

[@starnews3551]

Thank you ❤

[@mrhtutoring]

You're welcome 😊