Evaluate or simplify the expression without using a calculator.
-$10 \log \sqrt [ 5 ] { x }$
A) 5
B) $x ^ { - 1 / 5 }$
C) $x ^ { 1 / 5 }$
D) $x ^ { 5 }$

Question

Quizplus · Accepted Answer

The expression $10 \log \sqrt [ 5 ] { x }$ can be simplified using logarithmic and exponential rules. First, recognize that $\sqrt[5]{x} = x^{1/5}$. The property of logarithms that allows us to bring the exponent in front of the log gives us $10 \cdot \frac{1}{5} \log x$. Simplifying this, we get $2 \log x$, which implies we are looking for an expression equivalent to $x^{2 \cdot \frac{1}{2}} = x^{1} = x^{1/5}$, matching option C.

Evaluate or Simplify the Expression Without Using a Calculator 10log⁡x510 \log \sqrt [ 5 ] { x }10log5x​

Evaluate or Simplify the Expression Without Using a Calculator $10 \log \sqrt [ 5 ] { x }$