How do you simplify this expression?

Question

It gets confusing b/c of logs and exponents. Can someone help me explain how to do this.

8^log(8)x

Answer 1

got confused with this one too.

9^x =57

At first I square rooted but idk what to do now

Answer 2

^ 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

Answer 3

So what is the simplified expression of 8^log(8)x? I got confused.

Answer 4

8^log(8)x = x

I stated it clearly as one of the examples.

Similarly, log(8) 8^x = x