log-a-x-30-log-b-x-70-log-ab-x-

Question Number 197252 by sciencestudentW last updated on 11/Sep/23

lo \underset{a}{g} x = 30

lo \underset{b}{g} x = 70

lo \underset{a b}{g} x = ?

Answered by AST last updated on 11/Sep/23

\frac{l o g x}{l o g a} = 30; \frac{l o g x}{l o g b} = 70 \Rightarrow \frac{l o g b + l o g a}{l o g x} = \frac{1}{21}

\Rightarrow {l o g}_{a b} x = \frac{l o g x}{l o g a + l o g b} = 21

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