Use the properties of logarithms to evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.
A)2
B) $ \frac{1}{2} $
C) 72
D) $\log _ { 5 } 75$
E)None of these

Name: Use the properties of logarithms to evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator. A)2 B) $ \frac{1}{2} $ C) 72 D) $\log _ { 5 } 75$ E)None of these
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Quizplus · Accepted Answer

\begin{align*}
\log_5 75 - \log_5 3 &= \log_5 \frac{75}{3}\
&=\log_5 25\
&=\log_5 5^2\
&=2 \log_5 5\
&= 2 \quad 	ext{(since } \log_5 5 = 1 	ext{)}\
\end{align*}

Use the Properties of Logarithms to Evaluate log⁡575−log⁡53\log _ { 5 } 75 - \log _ { 5 } 3log5​75−log5​3

Use the Properties of Logarithms to Evaluate $\log _ { 5 } 75 - \log _ { 5 } 3$