Question

Explain how to solve 3^(x − 4) = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

5.631

Explanation:

Using the change of base formula log base b of y equals log y over log b

Log y (base b) = log y /log b

3^(x − 4) = 6

Taking the log of both sides

log 3^(x − 4) = log 6

using the logarithm law that states that

log a ^ x = x log a

x - 4 log 3 = log 6

x - 4 = log 6 / log 3

x - 4 = 1.630929754

x = 5.630929754

≈ 5.631

Answer 2

x = 4 + (log 6 / log 3)

x ≈ 5.631

Explanation:

3^(x − 4) = 6

Take log base 3 of both sides.

log₃ 3^(x − 4) = log₃ 6

x − 4 = log₃ 6

Use change of base formula.

x − 4 = log 6 / log 3

Solve for x.

x = 4 + (log 6 / log 3)

x ≈ 5.631