How do you solve $log_5x + log_3 x=1$ ?

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Answer 1 · 2018-05-07T08:48:41

$x=1.9211$

$log_5x+log_3 x=1$ can be written as

$logx/log5+logx/log3=1$

or $log3logx+log5logx=log3log5$

or $logx=(log3log5)/(log3+log5)$

or $x=10^((log3log5)/(log15))$

= $10^((0.4771*0.6990)/1.1761)$

= $10^0.2836$

= $1.9211$

How do you solve log_5x + log_3 x=1log_5x + log_3 x=1?