Solve the equation

In10^x=Log e^x +2

Now I got

xIn10 = xLog e +2

x 2.302585093 = x 0.434294481 + 2

x = 0.434294481 +2/2.302585093

so x = 1.0572066

But imputting this into the original equation is incorrect. Where did I go wrong? Help would be much appreciated thank you.

Simon