Answer
The two are the same, to three decimal places. This happens since the log functions are taken to different bases (but both sides of the equation are using that base in their logs).
Work Step by Step
$5^x=9$
$log {5^x} = log 9$
$x log 5 = log 9$
$x log 5/log 5 = log 9/log 5$
$x = log 9/log 5$
$x = .9542/log 5$
$x= .9542/ .69897$
$x= 1.36515$
$5^x=9$
$ln {5^x} = ln 9$
$x ln 5= ln 9$
$x ln 5/ln 5= ln 9/ln 5$
$x = ln9/ln 5$
$x =2.1972/ln 5$
$x =2.1972/1.6094$
$x=1.36523$
