Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 5 } x = - 3$
A) -15
B) $\frac { 1 } { 125 }$
C) 2
D) $\frac { 1 } { 243 }$.

Question

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 5 } x = - 3$
A)  -15 
B) $\frac { 1 } { 125 }$
C) 2
D) $\frac { 1 } { 243 }$.

Quizplus · Accepted Answer

The equation $\log_5 x = -3$ can be rewritten using the definition of a logarithm as $5^{-3} = x$. Calculating $5^{-3}$ gives $\frac{1}{5^3} = \frac{1}{125}$.

Use a Change of Base Formula to Evaluate the Given log⁡5x=−3\log _ { 5 } x = - 3log5​x=−3

Use a Change of Base Formula to Evaluate the Given $\log _ { 5 } x = - 3$