Question

If (5ˣ = y) and (x) is positive, which of the following equals (5y²) in terms of (x)?

a) (5²ˣ)
b) (5²ˣ⁺¹)
c) (25²ˣ)
d) (125²ˣ)

Answer 1

The correct expression for (5y²) in terms of (x), when (5ˣ = y), is (5²ˣ⁺ⁱ) because you square y to get (25ˣ) and multiply by 5 resulting in (5²ˣ + 1), which is option b).

Step-by-step explanation:

If given that (5ˣ = y) and (x) is positive, and we are asked to express (5y²) in terms of (x), we first need to find the expression for (y²). Since (5ˣ = y), squaring both sides of the equation gives us (5ˣ)² = y², which simplifies to (5²ˣ) or (25ˣ). Now, we multiply this by 5 to get (5× 25ˣ) or (5±× 25ˣ), since raising a base to a power and then raising it to another power means you multiply the exponents.

Therefore, the expression for (5y²) in terms of (x) is (5²ˣ⁺ⁱ), which is equivalent to (5²ˣ + 1) or option b) (5²ˣ⁺ⁱ).