Final answer:
To convert 7ˣ = 2401 into a logarithmic function, you rearrange it into the form log₇(2401) = x, which simplifies to x = 4 because 2401 is 7 to the power of 4.
Step-by-step explanation:
To write the equation 7x = 2401 as a logarithmic function, we need to express it in the form of logₙ(x) = y, where n is the base of the logarithm, x is the argument, and y is the exponent to which the base must be raised to get the argument. In this case, x is 7, y is x, and the argument is 2401, which can be expressed as 7⁴ because 7⁴ = 2401.
Therefore, the logarithmic form of the equation is log₇(2401) = x, and since 2401 is 7 to the power of 4, it simplifies to log₇(7⁴) = x. Using the property that logₙ(bᵃ) = a, we can then say that x = 4.