Verified answer

To find the exponent that completes the equation 432 = 24 * 3^x, we need to determine the value of x.

Given the equation:

432 = 24 * 3^x

To isolate the exponent term, we can divide both sides of the equation by 24:

432/24 = (24 * 3^x) / 24

Simplifying:

18 = 3^x

To determine the value of x, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) for this calculation:

ln(18) = ln(3^x)

Applying the logarithmic property:

ln(18) = x * ln(3)

Now, we can solve for x by dividing both sides of the equation by ln(3):

x = ln(18) / ln(3)

Using a calculator to evaluate the logarithms, we find:

x ≈ 1.55

Therefore, the exponent that completes the equation is approximately x = 1.55.