Question

Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

Answer 1

Remark
You could solve it using logs. Either base will do. They both will give you the same answer (I'll put the second solution before the first one).

Step one
Take the  log of both sides.

Log 37^x = log 12

Step Two
Using the power rule for logs, multiply x by the log(37)

x*log(37) = log (12)

Step three
Divide both sides by the log(37)

x = log(12) / log (37)
x = 1.079 / 1.568
x = 0.6882  <<<<< Answer

Use ln
ln 37^x = ln12    Take ln of both sides.
x*ln(37) = ln(12)  Multiply x (the power by ln(37)
x = ln(12) / ln(37) Divide by ln(37)
x = 2.485 / 3.611  
x = 0.6882 

You should be able to put the sentences together just the way I've done it.

Answer 2

Answer:

x=0.6882

In order to solve this problem, we must use logs, from either base.

We must first take the log of both sides, which will give us log 37^x=log 12. Then we have to multiply x by log(37), due to the power rule of logs, so we will now have x times log(37)=log (12). Afterwards, we have to divide both sides by log (37), so the equation will become x=log (12) / log (37) --> x=1.079/1.568, and our final simplifed answer will be 0.6882. We can then simply input the value of x into the original equation to check, and then we will know it is the correct answer.