Evaluate or simplify the expression without using a calculator.
-$10 \log \sqrt [ 4 ] { x }$
A) $x ^ { 1 / 4 }$
B) $x ^ { 4 }$
C) 4
D) $x ^ { - 1 / 4 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms and exponents, $10 \log \sqrt[4]{x} = 10 \log x^{1/4}$. Since $\log x^{1/4} = \frac{1}{4} \log x$, multiplying by 10 gives $10 \times \frac{1}{4} \log x = \frac{10}{4} \log x = 2.5 \log x$, which does not match any of the provided options directly. However, the initial interpretation aimed to simplify the expression directly to a form of $x$ raised to a power, which was a mistake. The correct simplification process should focus on the properties of logarithms that allow manipulation of the expression, but it seems there was a misunderstanding in the final step of simplification. The correct approach is to recognize that the expression simplifies based on the logarithm properties, but the provided options and the explanation do not align correctly with the standard logarithmic identities. The mistake was in attempting to directly equate the logarithmic expression to a power of $x$ without further manipulation involving logarithm properties that would lead to such a conclusion. The correct answer should involve recognizing that the expression simplifies through logarithmic properties, but none of the options directly represent the simplification of the given expression based on standard logarithmic and exponential rules. My initial explanation incorrectly attempted to directly match the logarithmic expression to the options provided without accurately applying the logarithmic properties to justify such a match.

Evaluate or Simplify the Expression Without Using a Calculator 10log⁡x410 \log \sqrt [ 4 ] { x }10log4x​

Evaluate or Simplify the Expression Without Using a Calculator $10 \log \sqrt [ 4 ] { x }$