Rewrite as a single logarithm.
-$$\frac { 1 } { 2 } \log _ { 2 } x ^ { 4 } + \frac { 1 } { 4 } \log _ { 2 } x ^ { 4 } - \frac { 1 } { 6 } \log _ { 2 } x$$
A) $\frac { 7 } { 6 } \log _ { 2 } x ^ { 8 }$
B) $\log _ { 2 } x ^ { 7 }$
C) $\log _ { 2 } x ^ { 17 / 6 }$
D) $\log _ { 2 } x ^ { 9 / 2 }$

Question

Quizplus · Accepted Answer

Combine the logarithms using properties: $\frac{1}{2} \log_2 x^4 + \frac{1}{4} \log_2 x^4 - \frac{1}{6} \log_2 x = \log_2 (x^4)^{1/2} + \log_2 (x^4)^{1/4} - \log_2 x^{1/6} = \log_2 x^2 + \log_2 x - \log_2 x^{1/6} = \log_2 (x^2 \cdot x \cdot x^{-1/6}) = \log_2 x^{17/6}$.

Rewrite as a Single Logarithm 12log⁡2x4+14log⁡2x4−16log⁡2x\frac { 1 } { 2 } \log _ { 2 } x ^ { 4 } + \frac { 1 } { 4 } \log _ { 2 } x ^ { 4 } - \frac { 1 } { 6 } \log _ { 2 } x21​log2​x4+41​log2​x4−61​log2​x

Rewrite as a Single Logarithm $\frac { 1 } { 2 } \log _ { 2 } x ^ { 4 } + \frac { 1 } { 4 } \log _ { 2 } x ^ { 4 } - \frac { 1 } { 6 } \log _ { 2 } x$