Solving exponential equation using laws of logarithm

Problem

Solve the exponential equation 4^x + 4^x + 1 = 40.

Solution

4^x + 4^x + 1 = 40

=> 2(4^x) = 39

=> 4^x = 39/2

Using the laws of logarithm

x log 4 = log 39 – log 2

x = (log 39 – log 2)/log 4

x = (1.59106 – 0.30103)/0.60206

x = 2.14206 (approx)