Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$$\frac { 1 } { 3 } \log _ { 3 } \left( x ^ { 6 } \right) + \frac { 1 } { 6 } \log _ { 3 } \left( x ^ { 6 } \right) - \frac { 1 } { 9 } \log _ { 3 } x$$
A) $\log _ { 3 } \left( x ^ { 7 } \right)$
B) $\frac { 7 } { 9 } \log _ { 3 } \left( x ^ { 12 } \right)$
C) $\log _ { 3 } \left( x ^ { 26 / 9 } \right)$
D) $\log _ { 3 } \left( x ^ { 9 / 2 } \right)$

Question

Quizplus · Accepted Answer

Using the logarithm power rule, $\log_b(m^n) = n\log_b(m)$, and the fact that logarithms of the same base can be added or subtracted by multiplying or dividing their arguments, the given expression simplifies to $\log_3(x^{26/9})$.

Write the Expression as a Single Logarithm with Coefficient 1 a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1

Write the Expression as a Single Logarithm with Coefficient 1 $a \neq 1 \text { and } b \neq 1$