Use the change of base formula to convert log _(8)12 to a ratio of logs base 7

Question

Use the change of base formula to convert log _(8)12 to a ratio of logs base 7

Answer 1

The formula we need to use is:

Log_a b = Log b/ Log a

Log₈ 12 = Log 12/ Log 8 ≈ 1.19498750024

In the problem, you want:

Log₇ X = Log₈ 12

and solve for X.

First, convert both sides to ratio of Logs:

Log X / Log 7 = Log 12 / Log 8

multiply Log 7 on both sides:

Log X = Log 7 (Log 12 / Log 8)

Log X = (0.845098040014)(1.19498750024) ≈ 1.00988159429

Make both sides as exponents of base 10:

10^(Log X) = 10^(1.00988159429)

That cancels the Log function and the base 10 of the left side:

X = 10.230140405