Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ nlog x
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
3 ln2 + ln8 = 2ln(4x)
ln2³ + ln8 = ln(4x)²
ln8 + ln8 = ln16x²
ln(8 × 8) = ln16x²
ln64 = ln16x², hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
