Question

Use the change of base formula to compute log5 9.

Round your answer to the nearest thousandth.

Answer 1

Let log₅9 = x
Then
5ˣ = 9 

Take log to base 10 of both sides.
log₁₀5ˣ = log₁₀9
x log₁₀5 = log₁₀9

Therefore
log₅9 = log₁₀9/log₁₀5
         = 0.9542/0.699
         = 1.3652

Answer: 1.365 (nearest thousandth)