Solve the system using the substitution method, if possible. $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$
A) $\left\{ \frac { 17 } { 5 } \right\}$
B) $\left\{ \frac { 9 } { 5 } \right\}$
C) $\{ - 3 \}$
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Question

Quizplus · Accepted Answer

Using the property of logarithms $\log a - \log b = \log \frac{a}{b}$, we can rewrite the equation as:

$$\log \frac{x+5}{x-2} = \log 6$$

Taking the exponential of both sides, we get:

$$\frac{x+5}{x-2} = 6$$

Solving for $x$, we obtain:

$$x+5 = 6(x-2)$$

$$x+5 = 6x-12$$

$$5x = 17$$

$$x = \frac{17}{5}$$

Therefore, the answer is B) $\left\{\frac{9}{5}\right\}$.

Solve the System Using the Substitution Method, If Possible log⁡(x+5)−log⁡(x−2)=log⁡6\log ( x + 5 ) - \log ( x - 2 ) = \log 6log(x+5)−log(x−2)=log6

Solve the System Using the Substitution Method, If Possible $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$