2log b​ 10−log b​ 5

The given expression is "2log_b 10 - log_b 5".

Step 1: Apply the power rule of logarithms to the first term. The power rule states that log_b a^n = n * log_b a. So, 2log_b 10 becomes log_b (10^2) = log_b 100.

Step 2: Now, the expression becomes "log_b 100 - log_b 5".

Step 3: Apply the quotient rule of logarithms. The quotient rule states that log_b (a / c) = log_b a - log_b c. So, log_b 100 - log_b 5 becomes log_b (100 / 5).

Step 4: Simplify the expression inside the logarithm. 100 / 5 = 20.

Step 5: So, the simplified expression is log_b 20.