Solve the equation.
-$\log _ { 6 } x + \log _ { 6 } ( x - 3 ) = 2$
A) $- 4.685,7.685$
B) $7.685$
C) $3.030$
D) No solution

Question

Quizplus · Accepted Answer

The equation can be rewritten using the property $\log_b(m) + \log_b(n) = \log_b(mn)$ as $\log_6(x(x-3)) = 2$. This implies $x(x-3) = 6^2 = 36$. Solving the quadratic equation $x^2 - 3x - 36 = 0$ gives the solutions $x = 7.685$ and $x = -4.685$. However, since logarithms are only defined for positive numbers, $x = -4.685$ is not valid. Thus, the only solution is $x = 7.685$.

Solve the Equation log⁡6x+log⁡6(x−3)=2\log _ { 6 } x + \log _ { 6 } ( x - 3 ) = 2log6​x+log6​(x−3)=2

Solve the Equation $\log _ { 6 } x + \log _ { 6 } ( x - 3 ) = 2$