Question

Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.

A.) −3.094
B.) −2.909
C.) 4.916
D.) 5.091

Answer 1

i know im late, but the answer is b. -2.909 :)

Answer 2

If you meant
`9^x+4=11`, then the answer is approximately 0.866.

If you meant
`9^(x+4)=11`, then the answer is approximately -2.909 which looks like what you meant based on the choices.

Explanation:

`9^x+4=11`

First step is to get the exponential part by itself. The part that has the variable exponent which is the
`9^x` term.

To do this we need to subtract 4 on both sides:

`9^x=11-4`

Simplify:

`9^x=7`

The equivalent logarithmic form is:

`\log_9(7)=x`

I always say to myself the logarithm is the exponent that is how I know what to put opposite the side containing the log.

Anyways if you don't have options for computing
`\log_b(a)` in your calculator you need to use the change of base formula.

`(\log(7))/(\log(9))=x`

So
`x \approx 0.8856`

I don't see this as a choice so maybe you actually meant the following equation:

`9^(x+4)=11`

Let's see if this is the correct interpretation.

So the exponential part is already isolated.

So we just need to put in the equivalent logarithmic form:

`\log_9(11)=x+4`

Now we subtract 4 on both sides:

`\log_9(11)-4=x`

Again if you don't have the option for computing
`\log_b(a)` in your calculator, you will have to use the change of base formula:

`(\log(11))/(\log(9))-4=x`

`x \approx -2.909`