Mike was 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 and how solving would be different if the bases were equal.

Question

anonymous · Answer

Hey, Mike. ll you have to do is take the log of both sides of your equation. You get
log 37^x = log 12
Then you can use a special rule of logarithms to change the right side to x log 37. Now we have
x log 37 = log 12
Now divide both sides by log 37.
x = log 12 / log 37. Put that in your calculator and you'll have the answer.

If the bases were equal it would be a lot easier. For example if it were 12^x = 12, the answer would be x = 1, since the right side can be rewritten as 12^1, and if the bases are equal we can just set the exponents equal to solve.

anonymous · Answer

Thank you so much, that was a great help! I don't have a calculator though, would it be too much trouble to ask you to give me that answer?

anonymous · Answer

@BangkokGarrett