Final answer:
To compare log_4(17) and log_5(24), we can use properties of logarithms. While we cannot determine exact values without calculation, we can infer that log_4(17) might potentially be smaller because 17 is closer to its base than 24 is to the base 5, but this is not a definitive method and requires further calculation.
Step-by-step explanation:
When comparing log4 17 and log5 24, it helps to understand that a logarithm is the power to which the base must be raised to produce the given number. To determine which logarithm is larger without the use of a calculator, we can use the property of logarithms that tells us the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers. This property allows us to compare the two given logarithms by understanding their relationship to a common base, such as base 10.
While we do not have the exact values of each logarithm, we can infer to some extent because 17 is closer to the base 4 than 24 is to the base 5. Since the closer the number is to the base, the smaller the logarithm, we might reason that log4 17 is smaller than log5 24. However, without calculation, this is just an educated guess and may not provide an accurate answer due to the non-linear nature of logarithmic functions.