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anonymous
 one year ago
Help please: log6(1/5√36)
anonymous
 one year ago
Help please: log6(1/5√36)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\log_{6} \frac{ 1 }{ \sqrt[5]{36} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So far I've done: dw:1442966236088:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so... what are you asked to do with \(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) ?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0"x"? kinda hard to find, since it isn't in the expression firstly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh hmm just saw it ... so is \(\bf \bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) =x\) then... ok

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup, says evaluate it. My notes said to set each equation to x and solve for it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well.... can we say...turn \(\large \bf \sqrt[5]{36}\) into a a value with a rational exponent? notice \(\large \sqrt[5]{36}\implies \sqrt[5]{6^2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0recall that \(\large { a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}} \\\quad \\ % rational negative exponent a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}} \implies \cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}\qquad\qquad % radical denominator \cfrac{1}{\sqrt[{\color{red} m}]{a^{\color{blue} n}}}= \cfrac{1}{a^{\frac{{\color{blue} n}}{{\color{red} m}}}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}} }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That makes sense. So now: 6^x = 6^2/5. Sixes cross out right? x = 2/5? Negative, since it was a fraction.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) =x\implies log_6\left( \cfrac{1}{6^{\frac{2}{5}}} \right)=x\implies log_{\color{red}{ 6}}\left( {\color{red}{ 6}}^{\frac{2}{5}} \right)=x \\ \quad \\ \textit{log cancellation rule } \qquad log_{\color{red}{ a}}{\color{red}{ a}}^x\implies x\qquad \qquad {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\qquad thus \\ \quad \\ \cfrac{2}{5}=x\)
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