Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}$

A) $\log _{x} \frac{x z^{3}}{y}$

B) $\log _{x} x z^{3} y$

C) $\log _{x} \frac{3 x z}{y}$

D) $\log _{x} \frac{x}{z^{3} y}$

Question

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}$

A) $\log _{x} \frac{x z^{3}}{y}$

B) $\log _{x} x z^{3} y$

C) $\log _{x} \frac{3 x z}{y}$

D) $\log _{x} \frac{x}{z^{3} y}$

Quizplus · Accepted Answer

The expression simplifies to $\log _{x} \frac{x z^{3}}{y}$ by using the logarithm properties: $\log_b a - \log_b c = \log_b \frac{a}{c}$ and $n \log_b a = \log_b a^n$.

Rewrite the Given Expression as a Single Logarithm (log⁡xx−log⁡xy)+3log⁡xz\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}(logx​x−logx​y)+3logx​z

Rewrite the Given Expression as a Single Logarithm $\left(\log _{\mathrm{x}} \mathrm{x}-\log _{\mathrm{x}} \mathrm{y}\right)+3 \log _{\mathrm{x}} \mathrm{z}$