Question

(90 POINTS) Explain how to solve 3ˣ⁻⁴ = 6 using the change of base formula. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Given: 3^(x − 4) = 6

To find: Solution to the given expression using change of base formula

Answer: The given expression is 3^(x − 4) = 6 Taking log on both sides, we get - log(3^(x − 4)) = log6

(x - 4) log3 = log6

x - 4 = log6/ log3

x - 4 =   (∵ change of base formula)

x - 4 = 1.631

x = 5.631

Thus x = 5.631 is the answer in the nearest thousandth.