To evaluate log base 7 of 17, we need to find the exponent that 7 must be raised to in order to obtain 17. In other words, we need to solve the equation 7^x = 17. This cannot be done algebraically, so we must use numerical methods or a calculator to approximate the solution. Using a calculator, we find that 7^1.455 ≈ 16.999, and 7^1.456 ≈ 17.035. Therefore, log base 7 of 17 is approximately 1.455. So, the answer is: 1.455.