Final answer:
The expression log₈ 8¹⁷ evaluates to 17 because 8 raised to the power of 17 is equal to 8¹⁷, and the base of the logarithm and the base of the exponent are the same.
Step-by-step explanation:
The question asks to evaluate the expression log₈ 8¹⁷. Logarithms measure how many times one number must be multiplied by itself to get another number.
In this case, we want to know what power we must raise 8 to in order to get 8¹⁷. Since any base raised to its corresponding logarithm equals the number itself, log₈ 8¹⁷ is asking for the exponent that makes 8 the result of raising 8 to that power. By the properties of logarithms, specifically the power rule (log(base)(number^exponent) = exponent*log(base)(number)), we conclude that the answer is simply 17, since log₈(8) is 1.