log b​ 3+5log b​ 2

The given expression is "log b​ 3 + 5log b​ 2".

Step 1: Apply the power rule of logarithms to the second term. The power rule states that logb(m^n) = n * logb(m). So, 5log b​ 2 becomes log b (2^5).

The expression now becomes "log b​ 3 + log b (32)".

Step 2: Apply the product rule of logarithms to the expression. The product rule states that logb(m) + logb(n) = logb(mn). So, log b​ 3 + log b (32) becomes log b (332).

The final simplified expression is "log b 96".