Solve the given exponential equation. Round answer to three decimal places.
-$$5 ^ { 2 x } + 5 ( x + 1 ) - 24 = 0$$
A) $\{ 0.683 \}$
B) $\{ 1.147 \}$
C) $\{ 1.099 \}$
D) $\{ 1.292 \}$

Question

Quizplus · Accepted Answer

This equation can be solved by recognizing it as a quadratic equation in disguise. Let $y = 5^x$, then the equation becomes $y^2 + 5y - 24 = 0$. Solving this quadratic equation gives $y = 3$ and $y = -8$. Since $y = 5^x$ and $5^x$ cannot be negative, we discard $y = -8$. Thus, $5^x = 3$. Taking the logarithm of both sides gives $x \log(5) = \log(3)$, and solving for $x$ gives $x \approx 0.683$.

Solve the Given Exponential Equation 52x+5(x+1)−24=05 ^ { 2 x } + 5 ( x + 1 ) - 24 = 052x+5(x+1)−24=0

Solve the Given Exponential Equation $5 ^ { 2 x } + 5 ( x + 1 ) - 24 = 0$