Rew rite as a single logarithm. A ssume all variables represent positive real numbers.
-$6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y$
A) $\log \frac{(\mathrm{x}+3)^{6}\left(\mathrm{x}^{2}+4\right)^{4}}{\sqrt[5]{\mathrm{y}}}$
B) $\frac{24}{5} \log \frac{(\mathrm{x}+3)\left(\mathrm{x}^{2}+4\right)}{\mathrm{y}}$
C) $\log \frac{(x+3)^{6} \sqrt[5]{y}}{\left(x^{2}+4\right)^{4}}$
D) $\frac{11}{5} \log \frac{(\mathrm{x}+3) \mathrm{y}}{\mathrm{x}^{2}+4}$

Question

Quizplus · Accepted Answer

The properties of logarithms allow for the combination of terms: coefficients become exponents inside the log, and subtraction of logs translates to division inside a single log. Thus, the correct expression is $\log \frac{(x+3)^{6} \sqrt[5]{y}}{\left(x^{2}+4\right)^{4}}$.

Rew Rite as a Single Logarithm 6log⁡(x+3)−4log⁡(x2+4)+15log⁡y6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y6log(x+3)−4log(x2+4)+51​logy

Rew Rite as a Single Logarithm $6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y$