Answer :
Answer:
If you meant [tex]9^x+4=11[/tex], then the answer is approximately 0.866.
If you meant [tex]9^{x+4}=11[/tex], then the answer is approximately -2.909 which looks like what you meant based on the choices.
Step-by-step explanation:
[tex]9^x+4=11[/tex]
First step is to get the exponential part by itself. The part that has the variable exponent which is the [tex]9^x[/tex] term.
To do this we need to subtract 4 on both sides:
[tex]9^x=11-4[/tex]
Simplify:
[tex]9^x=7[/tex]
The equivalent logarithmic form is:
[tex]\log_9(7)=x[/tex]
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 [tex]\log_b(a)[/tex] in your calculator you need to use the change of base formula.
[tex]\frac{\log(7)}{\log(9)}=x[/tex]
So [tex]x \approx 0.8856[/tex]
I don't see this as a choice so maybe you actually meant the following equation:
[tex]9^{x+4}=11[/tex]
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:
[tex]\log_9(11)=x+4[/tex]
Now we subtract 4 on both sides:
[tex]\log_9(11)-4=x[/tex]
Again if you don't have the option for computing [tex]\log_b(a)[/tex] in your calculator, you will have to use the change of base formula:
[tex]\frac{\log(11)}{\log(9)}-4=x[/tex]
[tex]x \approx -2.909[/tex]
