Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$4 e ^ { 2 x + 6 } = 20$$
A) 7.000
B) -2.626
C) -2.195
D) 3.805

Question

Quizplus · Accepted Answer

Taking the natural logarithm of both sides of the equation, we have: 
$$\ln(4e^{2x+6}) = \ln(20)$$
Using the properties of logarithms, we can simplify this to: 
$$\ln 4 + (2x+6)\ln e = \ln 20$$
Since $\ln e = 1$, we can further simplify to: 
$$2x+6 = \ln 20 - \ln 4 = \ln \frac{20}{4} = \ln 5$$
Dividing both sides by 2, we get: 
$$x = \frac{\ln 5 - 6}{2} \approx -2.195$$
Looking at the answer choices, we see that C is the closest to this value. We can also verify this by graphing both functions $y=4e^{2x+6}$ and $y=20$, and finding the intersection point, which appears to be around $x=-2.195$.

Use a Graph to Find an Approximate Solution to the Equation