Use properties of logarithms to evaluate the expression.
-$1000 ^ { \log _ { 10 } 9 }$
A) $10 ^ { 27 }$
B) 27
C) $\log 729$
D) 729

Question

Quizplus · Accepted Answer

The expression can be simplified using the property of logarithms $a^{ \log_a x } = x$. Here, $a = 10$ and $x = 9$, so $1000^{\log_{10} 9}$ simplifies to $10^{3 \cdot \log_{10} 9}$, which is $10^{\log_{10} 9^3}$, and since $9^3 = 729$, the expression equals 729.

Use Properties of Logarithms to Evaluate the Expression 1000log⁡1091000 ^ { \log _ { 10 } 9 }1000log10​9

Use Properties of Logarithms to Evaluate the Expression $1000 ^ { \log _ { 10 } 9 }$