Evaluate the given function.
-$$f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$$
A) $- 5$
B) 5
C) 2
D) $- 2$

Question

Evaluate the given function.  
-$$f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$$
A) $- 5$ 
B) 5 
C) 2 
D) $- 2$

Quizplus · Accepted Answer

When we plug in $\frac{1}{25}$ into the function $f(x)=\log_5{x}$, we get $f\left(\frac{1}{25}ight)=\log_5{\left(\frac{1}{25}ight)}$. Using the logarithmic property $\log_a{\left(\frac{1}{b}ight)}=-\log_a{b}$, we can simplify this expression to $f\left(\frac{1}{25}ight)=\log_5{\left(5^{-2}ight)}=-2\log_5{5}=\boxed{	ext{(D) }-2}$.

Evaluate the Given Function f(x)=log⁡5x,f(125)f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)f(x)=log5​x,f(251​)

Evaluate the Given Function $f ( x ) = \log _ { 5 } x , f \left( \frac { 1 } { 25 } \right)$