November 25, 2012

# 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)