Solve for $$ x $$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $$ e^{x+9}=15 $$

Question

UpStudy AI · Accepted Answer

We start with the equation
$$
e^{x+9} = 15.
$$

**Step 1:** Take the natural logarithm of both sides:
$$
\ln\left(e^{x+9}\right) = \ln(15).
$$

**Step 2:** Apply the property of logarithms $$ \ln(e^y) = y $$:
$$
x + 9 = \ln(15).
$$

**Step 3:** Solve for $$ x $$:
$$
x = \ln(15) - 9.
$$

**Step 4:** Now, compute the numerical value. Using a calculator,
$$
\ln(15) \approx 2.70805.
$$
Thus,
$$
x \approx 2.70805 - 9 \approx -6.29195.
$$

**Step 5:** Round $$ x $$ to the nearest hundredth:
$$
x \approx -6.29.
$$

The solution is:
$$
\boxed{x \approx -6.29}.
$$
$$ x \approx -6.29 $$

Solve for \( x \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{x+9}=15 \]