Final answer:
The equation 'log₁? = 4' cannot be properly re-written in exponential form since the base of a logarithm cannot be 1. Assuming a typographical error, a corrected version with a base 'b' (different from 1) would result in the equation b^4 = b when translated to exponential form.
Step-by-step explanation:
The student has asked to rewrite the following equation in exponential form: log₁? = 4. When rewriting a logarithmic equation in exponential form, the base of the logarithm becomes the base of the exponent in the result. So in this case, the correct rewriting of the equation in exponential form would be option c) 1 = 41.
This is because the logarithm represents the exponent to which the base (in this case, unknowably referred to as 1, which is probably a typo for a valid base since log base 1 is undefined) must be raised to result in the number inside the logarithm. However, given that the base is written as 1, this raises a point of confusion, as logarithms are not defined for a base of 1. Assuming this to be a typographical error and considering a valid base b (different from 1), if the equation was logb(b) = 4, then it would translate to b4 = b.