We can estimate the answer before we start to be somewhere between `2` and `3`, because 32 = 9 and `3^3= 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

logb (xn) = n logb 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.

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