Solve the exponential equation algebraically:

Question

2^x+1=5^2x

Answer 1

2^(x+1) = 5^2x.

Take log of both sides:
(x+1)log2 = 2xlog5,
0.301X + 0.301 = 1.398X,
0.301X - 1.398X = -0.301,
-1.097X = -0.301,
X = 0.2744.