Solve the problem.
-Given that $\log 5 \approx 0.6990$ and $\log 9 \approx 0.9542$, use the properties of logarithms to approximate the following. Do not use a calculator.
$\log \frac { 5 } { 81 }$
A) $2.6074$
B) $- 0.2115$
C) $0.7677$
D) $- 1.2094$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the properties of logarithms: $\log \frac { 5 } { 81 } = \log 5 - \log 81$. Since $\log 81 = \log 9^2 = 2\log 9$, we can substitute the given values to get $\log 5 - 2\log 9 = 0.6990 - 2(0.9542) = 0.6990 - 1.9084 = -1.2094$.

Solve the Problem log⁡5≈0.6990\log 5 \approx 0.6990log5≈0.6990 And log⁡9≈0.9542\log 9 \approx 0.9542log9≈0.9542

Solve the Problem $\log 5 \approx 0.6990$ And $\log 9 \approx 0.9542$