Find the exact value of the logarithmic expression without using a calculator.
$\log _ { 9 } \sqrt [ 3 ] { 9 }$
A) 3
B) $\frac { 1 } { 3 }$
C) 9
D) 27
E) None of these

Name: Find the exact value of the logarithmic expression without using a calculator. $\log _ { 9 } \sqrt [ 3 ] { 9 }$ A) 3 B) $\frac { 1 } { 3 }$ C) 9 D) 27 E) None of these
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Question

Find the exact value of the logarithmic expression without using a calculator. 
$\log _ { 9 } \sqrt [ 3 ] { 9 }$ 
A) 3
B) $\frac { 1 } { 3 }$
C) 9
D) 27
E) None of these

Quizplus · Accepted Answer

We can simplify the expression first:

$\log _ { 9 } \sqrt [ 3 ] { 9 } = \log _ { 9 } 9^{\frac13} = \frac13$

Therefore, the answer is (B).

Find the Exact Value of the Logarithmic Expression Without Using log⁡993\log _ { 9 } \sqrt [ 3 ] { 9 }log9​39​

Find the Exact Value of the Logarithmic Expression Without Using $\log _ { 9 } \sqrt [ 3 ] { 9 }$