Solve the equation. Write the answer in terms of the natural logarithm.

The solution set is .
(Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression. Use a comma
to separate answers as needed.)

Ask by Riley Best. in the United States

Mar 26,2025

Question

Solve the equation. Write the answer in terms of the natural logarithm.

The solution set is .
(Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression. Use a comma
to separate answers as needed.)

Ask by Riley Best. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

We start with the equation:

$$
e^{2x+3} = 15
$$

Take the natural logarithm of both sides:

$$
\ln\left(e^{2x+3}\right) = \ln(15)
$$

Using the property $$\ln\left(e^y\right) = y$$, we simplify the left side:

$$
2x + 3 = \ln(15)
$$

Next, isolate $$x$$ by subtracting 3 from both sides:

$$
2x = \ln(15) - 3
$$

Finally, divide both sides by 2:

$$
x = \frac{\ln(15) - 3}{2}
$$

The solution set is:

$$
\left\{ \frac{\ln(15) - 3}{2} \right\}
$$
The solution is $$ x = \frac{\ln(15) - 3}{2} $$.