Question

What exponential equation is equivalent to the logarithmic equation log(a)aˣ = x?

- a) e⁽ˣˡⁿ⁽ᵃ⁾⁾ = a
- b) aˣ = e⁽ˡⁿ⁽ᵃ⁾⁾
- c) aˣ = eˣ
- d) e⁽ˡⁿ⁽ᵃˣ⁾⁾ = x

Answer 1

The exponential equation equivalent to the logarithmic equation log(a)aˣ = x is aˣ = e⁽ˡⁿ⁽ᵃ⁾⁾.

Step-by-step explanation:

The exponential equation that is equivalent to the logarithmic equation log(a)aˣ = x is aˣ = e⁽ˡⁿ⁽ᵃ⁾⁾ (option b).

To understand why this is the correct answer, we can use the fact that the exponential and natural logarithm functions are inverse functions. Therefore, if we take the natural logarithm (ln) of both sides of the logarithmic equation, we get ln(a)aˣ = ln(x). Using the property ln(ab) = b ln(a), this simplifies to x ln(a) = ln(x), which can be rewritten as ln(x) = x ln(a). Now, if we raise both sides of this equation to the power of e, we get eˣ = aˣ. Therefore, the equivalent exponential equation is aˣ = eˣ.