Solve the equation. $2 e^{x+2}=5$
A) x = ln $\frac{5}{2}$ + 2
B) x = ln $\frac{2}{5}$ - 2
C) x = ln $\frac{2}{5}$ + 2
D) x = ln $\frac{5}{2}$ - 2

Question

Quizplus · Accepted Answer

Firstly, divide both sides by 2 to isolate the exponential term: 
$$e^{x+2} = \frac{5}{2}$$
Next, take the natural logarithm of both sides: 
$$\ln(e^{x+2}) = \ln\left(\frac{5}{2}\right)$$
By the properties of logarithms, we can simplify the left side as: 
$$x+2 = \ln\left(\frac{5}{2}\right)$$
Then, solve for $x$: 
$$x = \ln\left(\frac{5}{2}\right) - 2$$
So the answer is D.

Solve the Equation 2ex+2=52 e^{x+2}=52ex+2=5 A) X = Ln 52\frac{5}{2}25​ + 2 B) X = Ln

Solve the Equation $2 e^{x+2}=5$ A) X = Ln $\frac{5}{2}$ + 2
B) X = Ln