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

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Answer 1 · 2017-01-07T14:01:34

$x=5.585$

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

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