Answer:
1) [tex]9^{2}=81[/tex]
2) [tex]7=log_{2}(128)[/tex]
Step-by-step explanation:
1)
We need to use the property of power and logarithms, particularly this:
[tex]a=x^{log_{x}(a)}[/tex] (1)
So, let's take take the exponent:
[tex]9^{log_{9}}(\frac{1}{81})=9^{-2}[/tex]
[tex]\frac{1}{81}=9^{-2}[/tex]
now, we can write the negavitve power as:
[tex]\frac{1}{81}=\frac{1}{9^{2}}[/tex]
So, the aswer will be:
[tex]9^{2}=81[/tex]
2)
Applying equation 1, let's take log in base 2 on each side of the equation
[tex]log_{2}(2^{7})=log_{2}(128)[/tex]
using the power definition in log, we have:
[tex]7log_{2}(2)=log_{2}(128)[/tex]
Therefore, the answer is:
[tex]7=log_{2}(128)[/tex]
I hope it helps you!
