What is the value of log, base, 8, 512log 8​ 512?

The value of log base 8 of 512 can be found by solving the equation 8^x = 512.

Step 1: Write down the equation 8^x = 512.

Step 2: We know that 8 is 2^3 and 512 is 2^9. So we can rewrite the equation as (2^3)^x = 2^9.

Step 3: Simplify the equation to get 2^(3x) = 2^9.

Step 4: Since the bases are the same (both are 2), we can set the exponents equal to each other. So, 3x = 9.

Step 5: Solve for x by dividing both sides of the equation by 3. x = 9/3 = 3.

So, the value of log base 8 of 512 is 3.