log b​ 8+2log b​ 2

The given expression is log_b(8) + 2log_b(2).

Step 1: We know that log_b(a^n) = n*log_b(a). So, we can rewrite the expression as log_b(8) + log_b(2^2).

Step 2: Now, we know that 2^2 = 4 and 8 = 2^3. So, we can rewrite the expression as log_b(2^3) + log_b(4).

Step 3: Using the property of logarithms log_b(a) + log_b(c) = log_b(a*c), we can combine the two terms to get log_b(2^3 * 4).

Step 4: Simplifying the expression inside the log gives us log_b(32).

So, the simplified form of the given expression is log_b(32).