Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$
A) $125$
B) $250$
C) $3$
D) $25$
E) $496$

Name: Evaluate the expression without using a calculator. $\log _ { 5 } 500 - \log _ { 5 } 4$ A) $125$ B) $250$ C) $3$ D) $25$ E) $496$
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Question

Quizplus · Accepted Answer

Using the logarithmic property $\log_{a}(b)-\log_{a}(c)=\log_{a}{\frac{b}{c}}$, we have:
\begin{align*}
\log_{5}(500)-\log_{5}(4)&=\log_{5}\left(\frac{500}{4}ight)\
&=\log_{5}(125)\
&=\boxed{3}
\end{align*}

Evaluate the Expression Without Using a Calculator log⁡5500−log⁡54\log _ { 5 } 500 - \log _ { 5 } 4log5​500−log5​4

Evaluate the Expression Without Using a Calculator $\log _ { 5 } 500 - \log _ { 5 } 4$