Ed borrowed 1,500 for 4 months at 13.5 %. How much did he have to pay back under an add-on plan?

Answer 1

^ and log are inverse operations
x+8 - 8 = x
x/8 * 8 = x
(√x)^2 = x
log₈8^x = x
8^log₈x = x

The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier.

The definition of log₈x is that power of 8 which we need to get x.

Now, 9^x = 57 is a bit trickier. Recall that

log₉N is the power of 9 you need to get N. So,

log₉57 is the power of 9 you need to get 57.

Taking log₉ of both sides gives you

log₉9^x = log₉57

But since log₉9^x = x, you end up with
x = log₉57