Question

How do you solve `6^ { ( 3x - 2) } = 5^ { ( x - 2) }`?

Answer 1

`x=0.0968`

Explanation:

Taking logarithm on both sides of `6^((3x-2))=5^((x-2))`

`(3x-2)log6=(x-2)log5`

or `3log6x-2log6=log5x-2log5`

or `(3log6-log5)x=2log6-2log5`

or `x xx log((6xx6xx6)/5)=log((6xx6)/(5xx5))`

or `x=log1.44/log43.2=0.1583625/1.635484=0.0968`