Hello,
In class on monday we talked about solving exponential and logarithmic equations. We went about two ways of solving these. The first way was to rewrite as a log.
Which looks like this...

This is the original exponential equation.

Now we changed the exponential equation into a logarithmic equation. We did so by making it log base 2 to the 35 equals X. 

The next step involves doing the change of base formula. This means, we take log35 and divide it by log2 equalling X. When you do this out you get about 5.1. 

The second option you could do to solve, is to take the log of both sides.

Here is an example using the same exponential equation as before,

So, we started by taking the log of the 2^X. Then we took the log of 35. Then to get X alone, we divided by log2. 

So, now X=log35/log2

Then you re-arange the equation so that X=log base 2 to 35, which is the solution (seen below).

Then in Wednesdays class, we talked about when there are variables on both sides of an exponential equation. 

This is the original exponential equation. step by step directions are below.

  

First, we brought the exponents down, so it was (3x-1)log4=(x-2)log3

Then, we distributed the 4 and the 3 through the exponents

Then, we moved the terms like terms around so that we could factor out, so we got,

x(3log4-log3)= -2log3+log4

then we divided by the left side, which gave us the answer,

X= -2log3+4/3log4-log3

as a decimal it comes out to be about -.264986

Click here to see a video about solving logarithmic and exponential equations by YAYMATH