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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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1so... what are you asked to do with \(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) ?\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1"x"? kinda hard to find, since it isn't in the expression firstly

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1ohh 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.

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1well.... can we say...turn \(\large \bf \sqrt[5]{36}\) into a a value with a rational exponent? notice \(\large \sqrt[5]{36}\implies \sqrt[5]{6^2}\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1recall 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.

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) =x\implies log_6\left( \cfrac{1}{6^{\frac{2}{5}}} \right)=x\implies log_{\color{red}{ 6}}\left( {\color{red}{ 6}}^{\frac{2}{5}} \right)=x \\ \quad \\ \textit{log cancellation rule } \qquad log_{\color{red}{ a}}{\color{red}{ a}}^x\implies x\qquad \qquad {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\qquad thus \\ \quad \\ \cfrac{2}{5}=x\)
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