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.
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.