Question

Solve ln 5 + ln 2x = 3.
(1 point)
Responses

x equals start fraction e superscript 3 baseline minus 5 over 2 end fraction
Image with alt text: x equals start fraction e superscript 3 baseline minus 5 over 2 end fraction

x equals start fraction e superscript 3 baseline over 10 end fraction
Image with alt text: x equals start fraction e superscript 3 baseline over 10 end fraction

x equals start fraction 3 over ln 10 end fraction
Image with alt text: x equals start fraction 3 over ln 10 end fraction

x equals start fraction 3 minus ln 5 over 2 end fraction

Answer 1

To solve the equation \( \ln 5 + \ln 2x = 3 \), we can use the properties of logarithms.

First, we can combine the logarithms on the left side:

\[
\ln(5 \cdot 2x) = 3
\]

This simplifies to:

\[
\ln(10x) = 3
\]

Next, we exponentiate both sides to eliminate the natural logarithm:

\[
10x = e^3
\]

Now, we can solve for \( x \):

\[
x = \frac{e^3}{10}
\]

Thus, the solution is:

\[
x = \frac{e^3}{10}
\]

This corresponds to the response:

**x equals start fraction e superscript 3 baseline over 10 end fraction.**