Evaluate:log, base, 8, 32log 8​ 32

To evaluate the logarithm of 32 with base 8, we need to find the power to which 8 must be raised to get 32.

Step 1: Write down the logarithm log8(32)

Step 2: Convert the base to a power of 2 Since 8 is 2^3, we can rewrite the logarithm as: log2^3(2^5) Here, 32 is 2^5.

Step 3: Use the change of base formula The change of base formula is logb(a) = logc(a) / logc(b). We can use this to change the base to 2: log2(2^5) / log2(2^3)

Step 4: Simplify the logarithms The logarithm of a number to the same base is just the exponent, so we can simplify to: 5 / 3

So, log8(32) = 5/3.