Evaluate the expression without using a calculator. $\log _ { 6 } 864 - \log _ { 6 } 4$
A) $216$
B) $432$
C) $3$
D) $16$
E) $860$

Name: Evaluate the expression without using a calculator. $\log _ { 6 } 864 - \log _ { 6 } 4$ A) $216$ B) $432$ C) $3$ D) $16$ E) $860$
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Question

Quizplus · Accepted Answer

Using the logarithmic rule that $\log_a b - \log_a c = \log_a \frac{b}{c}$, we have $$\log_6 864 - \log_6 4 = \log_6 \frac{864}{4} = \log_6 216.$$ Writing $216$ as $6^3$, we get $$\log_6 6^3 = \boxed{3}.$$

Evaluate the Expression Without Using a Calculator log⁡6864−log⁡64\log _ { 6 } 864 - \log _ { 6 } 4log6​864−log6​4

Evaluate the Expression Without Using a Calculator $\log _ { 6 } 864 - \log _ { 6 } 4$