Question

How do you solve `12^(x-4)=3^(x-2)`?

Answer 1

`x=5.585`

Explanation:

As `12^(x-4)=3^(x-2)`, taking log on both sides, we get

`(x-4)log12=(x-2)log3`

or `xlog12-4log12=xlog3-2log3`

or `xlog12-xlog3=4log12-2log3`

or `x(log12-log3)=log((12^4)/(3^2))`

or `xlog4=log(4^2*12^2)=2log48`

or `x=(2log48)/(log4)=(2xx1.6812)/0.6021=5.585`