Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 6 } \sqrt { 10 x }$
A) $\frac { 1 } { 2 } \log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$
B) $\log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$
C) $\log _ { 6 } \sqrt { 10 } + \log _ { 6 } \sqrt { x }$
D) $\frac { 1 } { 2 } \log _ { 6 } 10 \mathrm { x }$

Question

Quizplus · Accepted Answer

The expression $\log _ { 6 } \sqrt { 10 x }$ can be rewritten using the properties of logarithms. The square root can be expressed as a power of $1/2$, and the logarithm of a product can be split into the sum of logarithms. Thus, it becomes $\frac { 1 } { 2 } \log _ { 6 } 10 + \frac { 1 } { 2 } \log _ { 6 } x$.

Write the Expression as Sums or Differences of Multiples of Logarithms