I was trying to find how many decimal digits the number $9^{10^{8.58}}$ has.
$9^{10^{8.58}} = 10^x$
$\log \space {9^{10^{8.58}}} = x$
$10^{8.58} \space\log \space 9 = x$
$x = 10^{8.55}$
Is this correct?
If I keep raising 9 to the power I iteratively calculate, the final power of ten will be shrinking.