Question

If $x=1+log2-log5,y=2log3$ and $z=loga-log5$; find the value of a, if $x+y=2z$.

Answer 1

$x=1+log2-log5$
$x=log10+log2-log5$
$x=log10\times 2-log5$
= $log\frac{20}{5}$

We have
$y=2log3$
= $log{3}^2$
= $log9$
Also, we have
$z=loga-log5$
= $log\frac{a}{5}$

$x+y=2z$

$log4+log9=2log\frac{a}{5}$
$log4+log9=log\frac{a^2}{25}$

$log36=log\frac{a^2}{25}$

$log\frac{a^2}{25}=36$

$a^2=36\times 25$

$a=30$