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Calculate $ \dfrac{\log_{a}9 - \log_{b}4}{\log_{a}3 - \log_{b}2}$
in Mathematics by Diamond (81,058 points) | 70 views

2 Answers

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(loga9−logb4)/(loga3−logb2)

= (loga3^2−logb2^2)/(loga3−logb2)

= (2loga3−2logb2)/(loga3−logb2)

=  2(loga3−logb2)/(loga3−logb2)

= 2
by Diamond (44,170 points)
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(log 9,base "a" - log 4, base "b") / (log 3, base "a" - log 2, base "b")

Write the number in exponential form with a base of 3.

(log 3^2, base "a" - log 2^2, base "b") - (log 3, base "a" - log 2, base "b")

Using formula: log b^c,base "a" = c * log b, base "a".

(2 log 3, base "a" - 2 log 2, base "b") / (log 3, base "a" - log 2, base "b"

Factor out 2 from the expression.

2(log 3, base "a" - log 2, base "b") / (log 3,base "a" - log 2, base "b") = 2

The Solution is 2

 

by Wooden (762 points)

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