How do you solve log(x-2)-log(2x-3)=log2log(x−2)−log(2x−3)=log2?

1 Answer
AJ
Mar 24, 2018

In the explanation. ..

Explanation:

Use the property of condensation of logarithmic function
Given,
log (x-2)-log (2x-3)=log (2)log(x−2)−log(2x−3)=log(2)
or, log ((x-2)/(2x-3)) = log (2)or,log(x−22x−3)=log(2)

or, 10^(log ((x-2)/(2x-3))=10^(log (2))or,10log(x−22x−3)=10log(2)
or, (x-2)/(2x-3)=2or,x−22x−3=2
or, (x-2)=2 (2x-3)or,(x−2)=2(2x−3)
or, (x-2)=4x-6or,(x−2)=4x−6
or, -2+6=4x-xor,−2+6=4x−x
or, 4=3xor,4=3x
:.x=4/3

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