log b​ 9−2log b​ 3

The given expression is log_b(9) - 2log_b(3).

Step 1: Use the power rule of logarithms to rewrite the second term. The power rule states that log_b(a^n) = nlog_b(a). So, 2log_b(3) becomes log_b(3^2) or log_b(9).

Step 2: Now, the expression becomes log_b(9) - log_b(9).

Step 3: Use the subtraction rule of logarithms to combine the two terms. The subtraction rule states that log_b(a) - log_b(c) = log_b(a/c). So, log_b(9) - log_b(9) becomes log_b(9/9).

Step 4: Simplify 9/9 to 1. So, the expression becomes log_b(1).

Step 5: The logarithm of any base b of 1 is always 0. So, log_b(1) = 0.

Therefore, the value of the given expression log_b(9) - 2log_b(3) is 0.