Question

Solve e2x = 50. Round to the thousandths place.

x = 0.849
x = 1.699
x = 1.956
x = 3.912

Answer 1

To solve the equation \( e^{2x} = 50 \), we can take the natural logarithm of both sides.

First, take the natural logarithm:

\[
\ln(e^{2x}) = \ln(50)
\]

Using the property of logarithms, \(\ln(e^a) = a\), we can simplify the left side:

\[
2x = \ln(50)
\]

Now, we can solve for \(x\) by dividing by 2:

\[
x = \frac{\ln(50)}{2}
\]

Next, calculate \(\ln(50)\):

Using a calculator, we find:

\[
\ln(50) \approx 3.912
\]

So:

\[
x = \frac{3.912}{2} \approx 1.956
\]

Rounding to the thousandths place, we get:

\[
x \approx 1.956
\]

Thus, the correct answer is:

\(\boxed{1.956}\)