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love history [14]
3 years ago
10

PLZ ANSWER ASAP! LOGS

Mathematics
1 answer:
UNO [17]3 years ago
4 0

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

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