Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$
A) $\log _ { 5 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$

B) $\frac { 19 } { 6 } \log _ { 5 } \frac { x } { ( x + 1 ) ^ { 2 } }$

C) $\log _ { 5 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$

D) $\log _ { 5 } \frac { x ^ { 19 / 6 } } { 2 ( x + 1 ) }$

Question

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$
A) $\log _ { 5 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$

B) $\frac { 19 } { 6 } \log _ { 5 } \frac { x } { ( x + 1 ) ^ { 2 } }$

C) $\log _ { 5 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$

D) $\log _ { 5 } \frac { x ^ { 19 / 6 } } { 2 ( x + 1 ) }$

Quizplus · Accepted Answer

Using the properties of logarithms, the expression can be simplified to $\log_5 \frac{x^{3 + \frac{1}{6}}}{(x+1)^2}$, which simplifies further to $\log_5 \frac{x^{19/6}}{(x+1)^2}$.

Express as the Logarithm of a Single Expression 3log⁡5x+16log⁡5x−2log⁡5(x+1)3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )3log5​x+61​log5​x−2log5​(x+1)

Express as the Logarithm of a Single Expression $3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$