Evaluate:log, base, 128, 32log 128​ 32

To evaluate the expression log base 128 of 32, we need to find the power to which 128 must be raised to get 32.

Step 1: Write the expression in exponential form. This gives us 128^x = 32.

Step 2: Simplify the bases. Both 128 and 32 can be written as powers of 2. This gives us (2^7)^x = 2^5.

Step 3: Simplify further. This gives us 2^(7x) = 2^5.

Step 4: Since the bases are equal, the exponents must also be equal. This gives us 7x = 5.

Step 5: Solve for x. This gives us x = 5/7.

So, log base 128 of 32 is 5/7.