Rewrite as a single logarithm. Assume all variables represent positive real numbers.
-$\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }$
A) $\log _ { b } \left( x ^ { 8 } - x \right)$
B) $\frac { \log _ { b } x ^ { 8 } } { \log _ { b } x }$
C) $\log _ { b } x ^ { 9 }$
D) $\log _ { b } x ^ { 7 }$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties. The first term is already in the desired form. The second term, $2 \log_b \sqrt{x}$, can be rewritten using the power rule of logarithms as $\log_b (\sqrt{x})^2 = \log_b x^1$. Therefore, the expression becomes $\log_b x^8 - \log_b x^1$, which simplifies to $\log_b \frac{x^8}{x^1} = \log_b x^7$, using the quotient rule of logarithms.

Rewrite as a Single Logarithm log⁡bx8−2log⁡bx\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }logb​x8−2logbx​

Rewrite as a Single Logarithm $\log _ { b } x ^ { 8 } - 2 \log b \sqrt { x }$