Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$2 \log _ { 6 } ( 6 p - 8 ) - 4 = - 2$
A) $\left\{ \frac { 7 } { 3 } \right\}$
B) $\left\{ - \frac { 7 } { 6 } \right\}$
C) $\left\{ \frac { 3 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

First, simplify the equation: $2 \log _ { 6 } ( 6 p - 8 ) - 4 = - 2$. Add 4 to both sides to get $2 \log _ { 6 } ( 6 p - 8 ) = 2$. Divide both sides by 2 to get $\log _ { 6 } ( 6 p - 8 ) = 1$. Convert to exponential form: $6^1 = 6p - 8$. Solve for $p$: $6 + 8 = 6p$, so $14 = 6p$, and $p = \frac{14}{6} = \frac{7}{3}$.

Solve the Equation 2log⁡6(6p−8)−4=−22 \log _ { 6 } ( 6 p - 8 ) - 4 = - 22log6​(6p−8)−4=−2

Solve the Equation $2 \log _ { 6 } ( 6 p - 8 ) - 4 = - 2$