log b​ 2+2log b​ 3

The given expression is log_b 2 + 2log_b 3.

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

Step 2: Now, the expression becomes log_b 2 + log_b 9.

Step 3: Use the product rule of logarithms to combine the two terms. The product rule states that log_b a + log_b c = log_b (ac). So, log_b 2 + log_b 9 becomes log_b (29) = log_b 18.

So, the simplified form of the given expression is log_b 18.