Question

PLZ ANSWER ASAP! LOGS

Answer 1

`\displaystyle \log_7(1)/(81)\approx -2.2`

Explanation:

We want to find:

`\displaystyle \log_7{(1)/(81)}`

First, using the quotient rule:

`\displaystyle \log_b(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`