Evaluate:log, base, 128, 64log 128​ 64

To evaluate the logarithm of 64 with base 128, we need to find the power to which 128 must be raised to get 64.

Step 1: Write down the logarithm log base 128 of 64

Step 2: Convert the bases to the same number We can convert both numbers to base 2, because both 128 and 64 are powers of 2. 128 = 2^7 and 64 = 2^6

Step 3: Substitute the converted bases into the logarithm log base 2^7 of 2^6

Step 4: Use the change of base formula The change of base formula is log_b(a) = log_c(a) / log_c(b). We can use this formula to change the base to 2. log base 2 of 2^6 / log base 2 of 2^7

Step 5: Simplify the logarithms The log base 2 of 2^6 is 6 and the log base 2 of 2^7 is 7. 6 / 7

So, log base 128 of 64 = 6/7.