anonymous
  • anonymous
Help please: log6(1/5√36)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\log_{6} \frac{ 1 }{ \sqrt[5]{36} }\]
anonymous
  • anonymous
So far I've done: |dw:1442966236088:dw|
jdoe0001
  • jdoe0001
so... what are you asked to do with \(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) ?\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Find x.
jdoe0001
  • jdoe0001
"x"? kinda hard to find, since it isn't in the expression firstly
jdoe0001
  • jdoe0001
ohh hmm just saw it ... so is \(\bf \bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) =x\) then... ok
anonymous
  • anonymous
Yup, says evaluate it. My notes said to set each equation to x and solve for it.
jdoe0001
  • jdoe0001
well.... 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
  • jdoe0001
recall 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
  • anonymous
That makes sense. So now: 6^x = 6^2/5. Sixes cross out right? x = 2/5? Negative, since it was a fraction.
jdoe0001
  • jdoe0001
close... one sec
jdoe0001
  • jdoe0001
\(\bf log_{6}\left( \cfrac{ 1 }{ \sqrt[5]{36} }\right) =x\implies log_6\left( \cfrac{1}{6^{\frac{2}{5}}} \right)=x\implies log_{\color{red}{ 6}}\left( {\color{red}{ 6}}^{-\frac{2}{5}} \right)=x \\ \quad \\ \textit{log cancellation rule } \qquad log_{\color{red}{ a}}{\color{red}{ a}}^x\implies x\qquad \qquad {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\qquad thus \\ \quad \\ -\cfrac{2}{5}=x\)
anonymous
  • anonymous
Thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.