Find the exact solution and a two-decimal-place approximation for it by using the Laws of Logarithms and the Change of Base Formula.

Question

4^(5 − x) = 6
(a) using the Laws of Logarithms
exact solution
approximate solution

(b) using the Change of Base Formula
exact solution
approximate solution

Answer 1

4^(5 − x) = 6
(5-x) log4 = log6
5-x = log6/log4
x = 5 - log6/log4

5-x = log₄6
x = 5 - log₄6