ln(x)=y <------> e^y=x

ln(x^y)=yln(x)

5^x=400

ln(5^x)=ln(400)

x*ln(5)=ln(400)

x=ln(400)/ln(5)    $${\frac{{ln}{\left({\mathtt{400}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} = {\mathtt{3.722\: \!706\: \!232\: \!293\: \!572\: \!2}}$$

5^{^3.7227062322935722026804262750 = 400.0000000000}

@headingnorth:/  Thanks for the math lesson! I didn't know how to figure it out mathematically.