If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.

Sure, here are the steps to solve the problem:

1. We know that log 10 to base 8 = X. This can be written as 8^X = 10.

2. We need to find log 5 to base 8. Let's denote this as Y. So, we have 8^Y = 5.

3. We can express 10 as 25. So, we can rewrite the equation from step 1 as 8^X = 25.

4. Now, we can use the property of logarithms that says the log of a product is the sum of the logs of its factors. So, we can write X = log 2 to base 8 + log 5 to base 8.

5. We know that log 2 to base 8 is a constant. Let's denote it as C. So, we have X = C + Y.

6. Solving for Y, we get Y = X - C.

So, log 5 to base 8 is equal to log 10 to base 8 minus log 2 to base 8, or X - C.