how do you do this?

1.08^x  =  3.076923

If the variable is an exponent, use logs (or lns):

log(1.08^x)  =  log(3.076923)

An exponent in a log expression, comes out as a multiplier:

x·log(1.08)  =  log(3.076923)

Divide by log(1.08):

x  =  log(3.076923) / log(1.08)

x  =  14.60388...

(You can use either the log key or the ln key.)

You find the value of x

$${{\mathtt{1.08}}}^{{\mathtt{x}}} = {\mathtt{3.076\: \!923}} \Rightarrow {{\mathtt{27}}}^{{\mathtt{x}}} = {\frac{{\mathtt{3\,076\,923}}{\mathtt{\,\times\,}}{{\mathtt{25}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}}{{\mathtt{64}}}} \Rightarrow {{\mathtt{27}}}^{{\mathtt{x}}} = {\frac{{\mathtt{3\,076\,923}}{\mathtt{\,\times\,}}{{\mathtt{25}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}}{{\mathtt{64}}}}$$