Final answer:
The value of x in the equation 81⁵ = 3ˣ is found by expressing 81 as a power of 3. Using exponent rules, the equation simplifies to 3²⁰ = 3ˣ, leading to the solution x = 20.
Step-by-step explanation:
To solve the equation 81⁵ = 3ˣ, we need to express 81 as a power of 3 since the right side of the equation is already in base 3. We know that 81 is equal to 3 to the power of 4 because 3*3*3*3 = 81 or 34 = 81. Now, we can rewrite the equation using this equivalency: 3²⁰ = 3ˣ.
Using the rule of exponents where (ap)q = apq, we get 34*5 = 3x. This simplifies to3²⁰ = 3ˣ Since the bases are the same, we can equate the exponents: 20 = x. Therefore, the value of x is 20, which corresponds to option A.