solve the exponential equation

Question

Sove the exponential equation and show work 

 

2^x+1=5^2x

Answer 1

2^x+1=5^2x

(x+1)log2=2xlog5

(x+1)/x=2log5/log2=log25/log2=C

x+1=Cx

1=(C-1)x

x=1/(C-1)=1/(log25/log2-1)

The remaining part of my former answer was nonsense.  This is now correct.