Answer:
[tex]\displaystyle \log_7\frac{1}{81}\approx -2.2[/tex]
Step-by-step explanation:
We want to find:
[tex]\displaystyle \log_7{\frac{1}{81}}[/tex]
First, using the quotient rule:
[tex]\displaystyle \log_b\frac{a}{c}=\log_b a-\log_b{c}[/tex]
We can rewrite our expression as:
[tex]=\log_7 1-\log_7 81[/tex]
The logarithm of 1 is always 0. Therefore:
[tex]=-\log_781[/tex]
We can rewrite this as:
[tex]=-\log_7 9\cdot 9[/tex]
Using the product rule:
[tex]\log_b ac=\log_ba+\log_bc[/tex]
This is equivalent to:
[tex]=-(\log_79+\log_79)[/tex]
Substitute:
[tex]=-(1.1+1.1)=-2.2[/tex]
