Question

Log 81 ______ = log 9

Answer 1

(log 81)/(log 9)=2log 9/log 9 = 2

Answer 2

To solve the equation log 81 (x) = log 9, we can use the properties of logarithms, specifically the change of base formula. The change of base formula states that for any positive numbers "a," "b," and "c" where "a" and "b" are bases and "c" is the number we are taking the logarithm of, the following holds:

log_a(c) = log_b(c) / log_b(a)

In this case, we want to find "x" such that log 81 (x) = log 9. Using the change of base formula with base 10:

log 81 (x) = log(x) / log(81)

Now, we have to express log(81) in terms of log(9):

81 = 9^2 log(81) = 2 * log(9)

Now, substitute back into the original equation:

log 81 (x) = log(x) / (2 * log(9))

Since the two logarithms are equal, we can simplify further:

x = 1/2

Therefore, log 81 (1/2) = log 9.