Question

PLZ ANSWER ASAP! LOGS

Answer 1

Answer:

$\displaystyle \log_7\frac{1}{81}\approx -2.2$

Step-by-step explanation:

We want to find:

$\displaystyle \log_7{\frac{1}{81}}$

First, using the quotient rule:

$\displaystyle \log_b\frac{a}{c}=\log_b a-\log_b{c}$

We can rewrite our expression as:

$=\log_7 1-\log_7 81$

The logarithm of 1 is always 0. Therefore:

$=-\log_781$

We can rewrite this as:

$=-\log_7 9\cdot 9$

Using the product rule:

$\log_b ac=\log_ba+\log_bc$

This is equivalent to:

$=-(\log_79+\log_79)$

Substitute:

$=-(1.1+1.1)=-2.2$