Question

Solve the equation y = ex for x.

Answer 1

x= y/e (or the last answer choice on your screen)

Explanation:

Answer 2

The transformed equation, with
`\( x \)` in terms of
`\( y \)`, is
`\( x = \ln(y) \)`. therefore, option C is correct

The image shows multiple choice options for a transformed version of the equation
`\( y = e^x \)`. To find the form of
`\( x \)` in terms of
`\( y \)`, we need to apply logarithmic operations because the equation involves the exponential function
`\( e^x \).`

Here's the step-by-step process to solve for
`\( x \)`:

1. Start with the given equation:
`\( y = e^x \).`

2. To solve for \( x \), take the natural logarithm (ln) of both sides of the equation to get the exponent on its own. This works because
`\( \ln(e^x) = x \)`, which is the inverse operation of the exponential function.

3. You'll end up with
`\( \ln(y) = x \)`.

So the transformed equation, with
`\( x \)` in terms of
`\( y \)`, is
`\( x = \ln(y) \)`. This corresponds to one of the choices given in the image. No further calculation is necessary, as this is a direct application of logarithmic properties.