Find the exact value of the logarithmic expression without using a calculator. $$\log _ { 9 } \sqrt [ 5 ] { 9 }$$
A) 5
B) 45
C) 9
D) $\frac { 1 } { 5 }$
E) None of these

Question

Find the exact value of the logarithmic expression without using a calculator. $$\log _ { 9 } \sqrt [ 5 ] { 9 }$$ 
A) 5
B) 45
C) 9
D) $\frac { 1 } { 5 }$
E) None of these

Quizplus · Accepted Answer

The expression can be simplified using the logarithm power rule, $\log_b (a^n) = n \log_b (a)$, where $b$ is the base of the logarithm, $a$ is the argument, and $n$ is the exponent. In this case, $\log_9 (\sqrt[5]{9})$ is equivalent to $\log_9 (9^{1/5})$, which simplifies to $\frac{1}{5} \log_9 (9)$. Since $\log_9 (9) = 1$, the expression simplifies to $\frac{1}{5}$.

Find the Exact Value of the Logarithmic Expression Without Using log⁡995\log _ { 9 } \sqrt [ 5 ] { 9 }log9​59​

Find the Exact Value of the Logarithmic Expression Without Using $\log _ { 9 } \sqrt [ 5 ] { 9 }$