How do you solve $log_5(x) + log_3(x) =1$ ?

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Answer 1 · 2015-12-04T17:37:03

I found: $x=1.921148$

We can change base:
$(ln(x))/(ln(5))+(ln(x))/(ln(3))=1$
$ln(x)(1/ln(5)+1/(ln(3)))=1$
$ln(x)[1.531574]=1$
$ln(x)=1/1.531574=0.652923$

use the definition of log:

$x=e^0.652923=1.921148$

How do you solve log_5(x) + log_3(x) =1log_5(x) + log_3(x) =1?