# How do you evaluate #log_9 9#?

##### 3 Answers

#### Explanation:

#"using the "color(blue)"law of logarithms"#

#•color(white)(x)log_b x=nhArrx=b^n#

#"let "log_9 9=n#

#"then "9=9^n#

#9^1=9^nrArrn=1#

#"this is a standard result"#

#•color(white)(x)log_b b=1#

#### Explanation:

Given:

Using the definition of logarithms, which states that:

if

So, we get:

#### Explanation:

We can use the logarithm rule

Since the base is the same as the thing we're taking the logarithm of, this evaluates to

In general, we know if we have

Then this can be rewritten as

In our scenario, our

We can rewrite this as

Since the bases are equivalent, so are the exponents. Thus,

This confirms for us that

Hope this helps!