Question

What is the true solution to 3 ln 2+ln 8=2ln(4x)

Answer 1

Answer: x=2 so B on edg

Answer 2

x = 2

Explanation:

Using the rules of logarithms

• log
`x^(n)` ⇔ 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 =
`√(4)` = 2