Answer: Explanation below.
Step-by-step explanation:
First of all you need to know how to convert a logarithm into an exponential expression. The property is:
[tex]log_Bx=n[/tex]
This is the same as: [tex]B^n=x[/tex]
Example 1:
[tex]log_99=[/tex]
We are trying to find what to raise 9 to, in order to get a result of 9.
[tex]9^x=9[/tex]
When you have same bases, you equal exponents.
[tex]x=1[/tex]
Therefore; [tex]log_99=1[/tex]
Example 2:
[tex]log_232=[/tex]
[tex]2^x=32[/tex]
In this case, we have to make sure both sides have the same base. 32 can have a base of 2 if expressed as: [tex]2^5[/tex] which is 2*2*2*2*2
Rewriting this example we have;
[tex]2^x=2^5[/tex]
Since we have the same base, we equal exponents.
[tex]x=5[/tex]
Therefore; [tex]log_232=5[/tex]
Example 3:
[tex]log_3729=[/tex]
[tex]3^x=729[/tex]
729 can have a base of 3 if expressed as: [tex]3^6[/tex]
[tex]3^x=3^6[/tex]
[tex]x=6[/tex]
