Question

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

Answer 1

In the explanation. ..

Explanation:

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

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