We can estimate the answer before we start to be somewhere between 2 and 3, because 3² = 9 and 3³ = 27. But how do we find the answer?

First we take the logarithm of both sides of the given equation:

log 3^x = log 12.7

Now, using the 3rd log rule

log_b (xⁿ) = n log_b x,

we have:

x log 3 = log 12.7

Now divide both sides by log 3:

x = (log 12.7)/(log 3)

= 2.3135

Is it correct? Checking in the original question, we have: 3^2.3135 = 12.7. Checks okay. Also, our answer is between 2 and 3 as we estimated before.