Estimate log 8 9 using the change of base formula.?

Question

Please give the answer to four decimal places.

Answer 1

y = log_8 (9) is the same thing as
8^y = 9

Take the log, base b, of both sides:

log_b(8^y) = log_b(9)
y log_b(8) = log_b(9)
y = log_b(9)/log_b(8)

If b=10, log_b(9) ≈ 0.9542425 and log_b(8) ≈ 0.9030900
so y = log_8(9) ≈ 0.9542425/0.9030900 = 1.0566 to four decimal places.

Of course, you will get the same result using logs for any legitimate base b. If you know what natural logs are, you should confirm that you get the same value for log_8 (9) by using natural logs as was obtained above using base-10 logs.