Asked by Amy

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

8^log(8)x
Answered by Amy
got confused with this one too.

9^x =57

At first I square rooted but idk what to do now
Answered by Steve
^ and log are inverse operations
x+8 - 8 = x
x/8 * 8 = x
(√x)^2 = x
log<sub>8</sub>8<sup>x</sup> = x
8<sup>log<sub>8</sub>x</sup> = 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 log<sub>8</sub>x is that power of 8 which we need to get x.

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

log<sub>9</sub>N is the power of 9 you need to get N. So,

log<sub>9</sub>57 is the power of 9 you need to get 57.

Taking log<sub>9</sub> of both sides gives you

log<sub>9</sub>9<sup>x</sup> = log<sub>9</sub>57

But since log<sub>9</sub>9<sup>x</sup> = x, you end up with
x = log<sub>9</sub>57
Answered by Amy
So what is the simplified expression of 8^log(8)x? I got confused.
Answered by Steve
8^log(8)x = x

I stated it clearly as one of the examples.

Similarly, log(8) 8^x = x
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