Question

What is 2log5(5x3)+1/3log5(x2+6) written as a single logarithm?

Answer 1

`\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2log_5(5x^3)+\cfrac{1}{3}log_5(x^2+6)\implies log_5([5x^3]^2)+log_5\left(\left[ x^2+6 \right]^{(1)/(3)} \right) \\\\\\ log_5\left( [5x^3]^2 \left[ x^2+6 \right]^{(1)/(3)}\right)\implies log_5\left( 25x^6\sqrt[3]{x^2+6} \right)`

Answer 2

The answer is B

Explanation:

Just making it easier on ed_g people.