Solve the equation. Find the exact solution. $\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1$
A) $5$
B) $4$
C) $3$
D) $7$
E) $1$

Question

Quizplus · Accepted Answer

Using the logarithmic identity $\log_a \frac{p}{q}=\log_a p - \log_a q$, we can rewrite the equation as:
$$\log_3 \frac{x+5}{x-2}=1$$
Writing this in exponential form, we get:
$$3^1=\frac{x+5}{x-2}$$
Simplifying, we get:
$$3x-6=x+5$$
$$2x=11$$
$$x=\frac{11}{2}$$

Therefore, the exact solution is $x=\frac{11}{2}$, which is not one of the answer choices. However, the closest answer choice is C) $3$.

Solve the Equation log⁡3(x+5)−log⁡3(x−2)=1\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1log3​(x+5)−log3​(x−2)=1

Solve the Equation $\log _ { 3 } ( x + 5 ) - \log _ { 3 } ( x - 2 ) = 1$