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) $${\frac{{ln}{\left({\mathtt{400}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} = {\mathtt{3.722\: \!706\: \!232\: \!293\: \!572\: \!2}}$$
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) $${\frac{{ln}{\left({\mathtt{400}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} = {\mathtt{3.722\: \!706\: \!232\: \!293\: \!572\: \!2}}$$
@headingnorth:/ Thanks for the math lesson! I didn't know how to figure it out mathematically.