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.

Question

Abigail

Mathematics

27 February, 23:14

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.

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Wendy Crawford · Answer 1

The equation is 37ˣ = 12

First, logarithms should be taken on each side. Any base of the logarithms will suffice but we will use base 10 since it is easily available on calculators.

log (37ˣ) = log (12)

In logarithms, the power of the number comes down as a coefficient of the logarithm. So,

xlog (37) = log (12)

Now, we divide on both sides by log (37) to get x alone

x = log (12) / log (37)

using a calculator, we obtain,

x = 0.688