Question

How do you do this I don't understand and the other websites are not helping

Answer 1

`\bf \textit{Logarithm of rationals}\\\\ log_{{ a}}\left( (x)/(y)\right)\implies log_{{ a}}(x)-log_{{ a}}(y) \\\\\\ \textit{Logarithm of exponentials}\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\\\ \textit{also recall that }\qquad a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \textit{and that }\qquad log_x(x)=1\\\\ -------------------------------\\\\`


`\bf log_5\left( \cfrac{125}{√(x+6)} \right)\qquad \begin{cases} 125=5^3\\\\ √(x+6)=(x+6)^{(1)/(2)} \end{cases}\implies log_5\left[ \cfrac{5^3}{(x+6)^{(1)/(2)}} \right] \\\\\\ log_5(5^3)-log_5\left[ (x+6)^{(1)/(2)} \right]\implies 3log_5(5)-\cfrac{1}{2}log_5(x+6) \\\\\\ 3(1)-\cfrac{1}{2}log_5(x+6)\implies 3-\cfrac{log_5(x+6)}{2}`