Solve the exponential equation below algebraically. Round your result to three decimal places.
$$\frac { 375 } { 1 + e ^ { x } } = 125$$
A) $2.697$
B) $2.883$
C) $3.303$
D) $- 1.086$
E) $0.693$

Question

Quizplus · Accepted Answer

To solve the equation, multiply both sides by $1 + e^x$ to get $375 = 125(1 + e^x)$. Simplify to $375 = 125 + 125e^x$. Subtract 125 from both sides to get $250 = 125e^x$. Divide both sides by 125 to get $2 = e^x$. Taking the natural logarithm of both sides gives $x = \ln(2)$, which is approximately $0.693$.

Solve the Exponential Equation Below Algebraically 3751+ex=125\frac { 375 } { 1 + e ^ { x } } = 1251+ex375​=125

Solve the Exponential Equation Below Algebraically $\frac { 375 } { 1 + e ^ { x } } = 125$