Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
-$$e ^ { 2 x } + e ^ { x } - 6 = 0$$
A) $0.69$
B) $0.69,1.10$
C) $1.10,0.14$
D) $0.14$

Question

Quizplus · Accepted Answer

To solve the exponential equation $e^{2x} + e^x - 6 = 0$, we can substitute $u = e^x$, which gives us a quadratic equation $u^2 + u - 6 = 0$. Factoring or using the quadratic formula, we find the roots of this equation are $u = 2$ and $u = -3$. Since $u = e^x$, and $e^x$ cannot be negative, we discard $u = -3$ and keep $u = 2$. Solving $e^x = 2$ gives $x = \ln(2)$, which is approximately $0.69$ when rounded to two decimal places.

Solve the Exponential Equation e2x+ex−6=0e ^ { 2 x } + e ^ { x } - 6 = 0e2x+ex−6=0

Solve the Exponential Equation $e ^ { 2 x } + e ^ { x } - 6 = 0$