log-3-a-log-4-b-log-5-36-

Question Number 197250 by sciencestudentW last updated on 11/Sep/23

\log 3 = a

\log 4 = b

lo \underset{5}{g 36} = ?

Answered by AST last updated on 11/Sep/23

\frac{l o g 3}{l o g 2 + l o g 5} = a

\frac{2 l o g 2}{l o g 2 + l o g 5} = b \Rightarrow l o g 2 (2 - b) = b l o g 5

{l o g}_{5} 36 = \frac{2 l o g 2 + 2 l o g 3}{l o g 5} = \frac{2 l o g 2 + 2 a l o g 2 + 2 a l o g 5}{l o g 5}

= 2 (\frac{b}{2 - b}) + \frac{2 a b}{2 - b} + 2 a = \frac{2 b}{2 - b} + 2 a (\frac{2}{2 - b}) = \frac{2 b + 4 a}{2 - b}

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