If-a-2-b-2-12-then-log-3-b-a-a-2-b-1-c-0-d-1-e-2-

Question Number 65971 by gunawan last updated on 07/Aug/19

If \frac{a^{2}}{b^{2}} = 12 then \log (^{3} \sqrt{\frac{b}{a}}) = . .

a . - 2

b . - 1

c . 0

d . 1

e . 2

Answered by MJS last updated on 07/Aug/19

\ln \sqrt[3]{\sqrt{12}} = \ln \sqrt[6]{12} = \frac{\ln 12}{6} = \frac{\ln 2}{3} + \frac{\ln 3}{6}

Answered by kaivan.ahmadi last updated on 07/Aug/19

\frac{a^{2}}{b^{2}} = 12 \Rightarrow {(\frac{b}{a})}^{2} = \frac{1}{12} \Rightarrow \frac{b}{a} = \sqrt{\frac{1}{12}} \Rightarrow

\sqrt[3]{\frac{b}{a}} = \sqrt[6]{\frac{1}{12}} = {(\frac{1}{12})}^{\frac{1}{6}} = 12^{- \frac{1}{6}} \Rightarrow

l o g (\sqrt[3]{\frac{b}{a}}) = l o g 12^{- \frac{1}{6}} = - \frac{1}{6} l o g 12 = - {l o g}_{6} 12

= - ({l o g}_{6} 6 + {l o g}_{6} 2) = - 1 - {l o g}_{6} 2