Evaluate the function at the indicated value of $x = 3$ .
$f ( x ) = \log _ { 243 } x$
A) $\frac { 1 } { 5 }$
B)-5
C) $- \frac { 1 } { 5 }$
D)0
E)5

Question

Evaluate the function at the indicated value of $x = 3$ . 
 $f ( x ) = \log _ { 243 } x$ 
A) $\frac { 1 } { 5 }$
B)-5
C) $- \frac { 1 } { 5 }$
D)0
E)5

Quizplus · Accepted Answer

The function $f(x) = \log_{243} x$ evaluated at $x = 3$ can be rewritten as $\log_{243} 3$. Since $243 = 3^5$, the equation becomes $\log_{3^5} 3$, which simplifies to $\frac{1}{5}$ because $\log_{b^k} a = \frac{1}{k} \log_b a$ when $a = b$.

Evaluate the Function at the Indicated Value Of x=3x = 3x=3

Evaluate the Function at the Indicated Value Of $x = 3$