log b​ 2+3log b​ 3

The given expression is "log b​ 2 + 3log b​ 3".

Step 1: Apply the power rule of logarithms to the second term. The power rule states that logb(m^n) = n * logb(m). So, 3log b​ 3 becomes log b (3^3).

The expression now becomes "log b​ 2 + log b (27)".

Step 2: Apply the product rule of logarithms to the expression. The product rule states that logb(m) + logb(n) = logb(m*n).

So, "log b​ 2 + log b (27)" becomes "log b (2*27)".

Step 3: Simplify the expression.

2*27 = 54.

So, "log b (2*27)" becomes "log b 54".

Therefore, the simplified form of the given expression "log b​ 2 + 3log b​ 3" is "log b 54".