Use the properties of logarithms to simplify the expression. $\log _ { 5 } 5 ^ { 5 }$
A)0
B) $- \frac { 1 } { 5 }$
C) $\frac { 1 } { 5 }$
D)-5
E)5

Question

Use the properties of logarithms to simplify the expression.  $\log _ { 5 } 5 ^ { 5 }$ 
A)0
B) $- \frac { 1 } { 5 }$
C) $\frac { 1 } { 5 }$
D)-5
E)5

Quizplus · Accepted Answer

The property of logarithms that applies here is $\log_b(b^x) = x$, where $b$ is the base of the logarithm and $b^x$ is the argument. Applying this property to $\log_5(5^5)$, we get $5$ because the base (5) and the base of the argument (5) are the same, and the exponent of the argument is $5$.

Use the Properties of Logarithms to Simplify the Expression log⁡555\log _ { 5 } 5 ^ { 5 }log5​55

Use the Properties of Logarithms to Simplify the Expression $\log _ { 5 } 5 ^ { 5 }$