Question

How do you solve `log_7 12 = x`?

Answer 1

From `log` definition, we have that `log_ba=c <=>b^c=a`

Explanation:

Thus,

`log_7(12)=x <=> 7^x=12`

Now, we can apply `log` on both sides of the equation.

`log7^x=log12`

Another `log` rule states that `log_ba^n=n*log_ba`, so:

`x*log7=log12`
`x=log12/log7` (both on base 10 or base `e` or whatever base you end up finding convenient! It really does not matter!)

Using a calculator, as these are not exact expressions, you can find the approximate value of

`x~=1.277`