which expression represents $\frac{1}{3}log x-log5$ as a single logarithm?\na $log(\frac{x^{3}}{5})$\nb…

which expression represents $\frac{1}{3}log x-log5$ as a single logarithm?\na $log(\frac{x^{3}}{5})$\nb $log\frac{sqrt3{x}}{5}$\nc $log(\frac{1}{3}+x - 5)$\nd $log(sqrt3{x}-5)$

which expression represents $\frac{1}{3}log x-log5$ as a single logarithm?\na $log(\frac{x^{3}}{5})$\nb $log\frac{sqrt3{x}}{5}$\nc $log(\frac{1}{3}+x - 5)$\nd $log(sqrt3{x}-5)$

Answer

Explanation:

Step1: Apply power - rule of logarithms

Recall that $n\log a=\log(a^{n})$. So, $\frac{1}{3}\log x=\log(x^{\frac{1}{3}})=\log(\sqrt[3]{x})$.

Step2: Apply quotient - rule of logarithms

Recall that $\log a-\log b = \log(\frac{a}{b})$. Since we have $\log(\sqrt[3]{x})-\log5$, by the quotient - rule, it is equal to $\log(\frac{\sqrt[3]{x}}{5})$.

Answer:

B. $\log\frac{\sqrt[3]{x}}{5}$