Big Ideas Math [IM3]: 5.5 - Solving Exponential and Logarithmic Equations (Lecture & Problem Set)

As we solve exponential and logarithmic equations, we take properties from previous sections and use them here. Get bases to match on both sides of the equations and solve for the variables inside your functions, and in cases when bases can't match then attempt to convert forms (use the log function when changing up an exponential equation, or rewrite a logarithm into exponential form). Be weary of your domain when solving for x when it comes to log equations.

This is one of those sections where, as a math teacher, I am extremely comfortable with working around exponents, logarithms, fractions, decimals, and negatives any which way the problem presents itself. However, this may be one of the first experiences prior to pre-calc and calculus where you feel behind the problem at every which turn, and it is completely understandable. In short, this solution guide video is made for you, and I hope you benefit off it.

I acknowledge that I may completely outdo myself when it comes to showing different ways that a problem can be solved, but it is always with the intent that you need to know logarithms can be expressed in more than one way and it is all interconnected. I hope what I show genuinely proves that, and you end up finding a method for yourself that works best in each given problem.

Admittedly, some problems become extremely tricky, especially the #67-72 block of critical thinking questions (and I know for a fact there are condensed ways of doing those problems, but I didn't want to experiment with it and be wrong on video, so I chose a safe option for them).

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*PDF DOWNLOADS*

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*TIMESTAMPS (separated by section)*

(0:00:00) Introduction
(0:01:15) Lecture overview
(0:16:29) Problem #1-4
(0:20:46) Problem #5-16
(0:35:37) Problem #17-18
(0:42:40) Problem #19-20
(0:50:36) Problem #21-32
(1:01:27) Problem #33-40
(1:17:14) Problem #41-42
(1:19:58) Problem #43
(1:29:35) Problem #44
(1:30:54) Problem #45
(1:33:12) Problem #46
(1:34:25) Problem #47-54
(1:44:32) Problem #55
(1:47:43) Problem #56-58
(1:59:47) Problem #59-62
(2:06:24) Problem #63
(2:12:13) Problem #64
(2:13:57) Problem #65
(2:17:39) Problem #66
(2:22:20) Problem #67-72
(2:40:31) Problem #73
(2:42:45) Problem #74

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*BIG IDEAS MATH (IM3) PLAYLIST*