Question

If $p=log20$ and $q=log25$, find the value of $x$, if $2log(x+1)=2p-q$.

Answer 1

$p=log20$ and $q=log25$
We also have
$2log(x+1)=2log20-log25$

$2log(x+1)=2p-q$

$log(x+1{)}^2=log{20}^2-log25$

$log(x+1{)}^2=log400-log25$

$log(x+1{)}^2=log16$

$log(x+1{)}^2=log{4}^2$

$x+1=4$

$x=3$