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.