Solve the exponential equation by using the property that $b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b 0 \text { and } b \neq 1 \text {. }$
$6.8 ^ { x - 3 } = 6.8 ^ { 2 x + 21 }$
A) $\left\{ 6.8 ^ { - 24 } \right\}$
B) { }
C) $\{ 9 \}$
D) $\{ - 24 \}$

Question

Solve the exponential equation by using the property that $b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b > 0 \text { and } b \neq 1 \text {. }$ 
$6.8 ^ { x - 3 } = 6.8 ^ { 2 x + 21 }$
A) $\left\{ 6.8 ^ { - 24 } \right\}$
B) {   }
C) $\{ 9 \}$
D) $\{ - 24 \}$

Quizplus · Accepted Answer

Given the property $b ^ { x } = b ^ { y } \implies x = y$ for $b > 0$ and $b \neq 1$, we can set the exponents equal to each other since the bases are the same. Thus, $x - 3 = 2x + 21$. Solving for $x$ gives $x = -24$.

Solve the Exponential Equation by Using the Property That bx=by implies x=y, for b>0 and b≠1. b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b > 0 \text { and } b \neq 1 \text {. }bx=by implies x=y, for b>0 and b=1.

Solve the Exponential Equation by Using the Property That $b ^ { x } = b ^ { y } \text { implies } x = y \text {, for } b > 0 \text { and } b \neq 1 \text {. }$