log b​ 2+5log b​ 2

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

Step 1: Understand the properties of logarithms The properties of logarithms that we will use are:

• log_b(a) + log_b(c) = log_b(ac)
• n*log_b(a) = log_b(a^n)

Step 2: Apply the properties First, we can apply the second property to the second term of the expression to get: log_b(2) + log_b(2^5)

Step 3: Simplify the expression 2^5 equals 32, so the expression becomes: log_b(2) + log_b(32)

Step 4: Apply the first property Now we can apply the first property to combine the two terms into one: log_b(2*32)

Step 5: Simplify the expression 2*32 equals 64, so the final simplified expression is: log_b(64)

So, "log b​ 2 + 5log b​ 2" simplifies to "log_b(64)".