Question

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

Answer 1

Mike would first have to divid 37 from 12 and he would then find x

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.