![\bf \textit{Logarithm of rationals}\\\\ log_{{ a}}\left( \frac{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\\\\ -------------------------------\\\\](/tpl/images/0470/8621/feb0a.png)
![\bf log_5\left( \cfrac{125}{\sqrt{x+6}} \right)\qquad \begin{cases} 125=5^3\\\\ \sqrt{x+6}=(x+6)^{\frac{1}{2}} \end{cases}\implies log_5\left[ \cfrac{5^3}{(x+6)^{\frac{1}{2}}} \right] \\\\\\ log_5(5^3)-log_5\left[ (x+6)^{\frac{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}](/tpl/images/0470/8621/c3043.png)
How do you do this i don't understand and the other websites are not
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Mathematics, 25.01.2020 22:31 ekautz9675
How do you do this i don't understand and the other websites are not
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