Question

select the correct answer.
what is the solution to this equation?
\log_{6} x + \log_{6} 3 = \log_{6} (x + 1)
a. \\( x = \frac{3}{2} \\)
b. \\( x = 1 \\)
c. \\( x = \frac{1}{3} \\)
d. \\( x = \frac{1}{2} \\)

Explanation:

Step1: Apply log product rule

$\log_6(x \cdot 3) = \log_6(x+1)$

Step2: Cancel log (same base)

$3x = x + 1$

Step3: Isolate x terms

$3x - x = 1$

Step4: Solve for x

$2x = 1 \implies x = \frac{1}{2}$

Answer:

D. $x = \frac{1}{2}$