Question

What is the solution to this equation?

Answer 1

Answer:

D

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log ($\frac{x}{y}$ )

log $x^{n}$ = nlog x

$log_{b}$ x = n ⇒ x = $b^{n}$

Given

$log_{3}$ (4x) - 2$log_{3}$ x = 2

$log_{3}$ (4x) - $log_{3}$ x² = 2

$log_{3}$ ($\frac{4x}{x^2}$ ) = 2

$log_{3}$ ($\frac{4}{x}$ ) = 2

$\frac{4}{x}$ = 3² = 9 ( multiply both sides by x )

4 = 9x ( divide both sides by 9 )

$\frac{4}{9}$ = x → D