$c=10000000000000000000000\times 100000000^{x}$
$Im(\ln(100000000^{x}))-8\ln(10)Im(x)=0$

$x=\frac{\log(c)-22}{8}$
$c\neq 0$

$c=10000000000000000000000\times 100000000^{x}$

$x=\frac{\log(c)-22}{8}$
$c>0$