MIke is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

Question

Mathematics

Wise

22 December, 19:57

MIke is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

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Answers (2)

Know the Answer?

Parker Blake · Answer 1

Parker Blake 22 December, 21:24

0

Start by getting the x to be alone

Natalee Brandt · Answer 2

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.