Question-164806

Question Number 164806 by saboorhalimi last updated on 22/Jan/22

Commented by cortano1 last updated on 22/Jan/22

\log_{12} (3) = a \Rightarrow \log_{3} (12) = \frac{1}{a}

\Rightarrow 1 + 2 \log_{3} (2) = \frac{1}{a}

\Rightarrow \log_{3} (2) = \frac{1 - a}{2 a}

\Rightarrow \frac{\log_{5} (2)}{\log_{5} (3)} = \frac{1 - a}{2 a}

\Rightarrow \log_{5} (2) = (\frac{1 - a}{2 a}) \log_{5} (3)

Commented by cortano1 last updated on 22/Jan/22

\log_{12} (3) = \frac{\log_{5} (3)}{\log_{5} (12)} = a

\Rightarrow \log_{5} (3) = a (\log_{5} (3) + 2 \log_{5} (2))

\Rightarrow (1 - a) \log_{5} (3) = 2 a \log_{5} (2)

\Rightarrow \log_{5} (2) = \frac{(1 - a)}{2 a} \log_{5} (3)

Commented by mr W last updated on 22/Jan/22

i s \log_{5} 3 b e t t e r t h a n \log_{5} 2 ?

Commented by cortano1 last updated on 22/Jan/22

y e s

Commented by mr W last updated on 22/Jan/22

a n d h o w t o g e t \log_{5} 3 ?

Commented by cortano1 last updated on 22/Jan/22

b y c a l c u l a t o r

Commented by cortano1 last updated on 22/Jan/22

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Answered by MJS_new last updated on 22/Jan/22

\log_{12} 3 = a \Leftrightarrow \log_{5} 2 = b

or else solve this : \sqrt[17]{29} = α, \sqrt[13]{7} = ?

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