2log b​ 4−log b​ 2

The given expression is 2log_b(4) - log_b(2).

Step 1: Use the power rule of logarithms to simplify the first term. The power rule states that log_b(a^n) = n*log_b(a). So, 2log_b(4) becomes log_b(4^2) = log_b(16).

Step 2: Now, the expression becomes log_b(16) - log_b(2).

Step 3: Use the quotient rule of logarithms to combine the two terms. The quotient rule states that log_b(a) - log_b(c) = log_b(a/c). So, log_b(16) - log_b(2) becomes log_b(16/2) = log_b(8).

So, the simplified form of the given expression is log_b(8).