Question

What is the true solution to 3ln2+ln8=2ln(4x)? a.x=1 b.x=2 c.x=4 d.x=8

Answer 1

x = 2

Explanation:

Using the rules of logarithms

• log x + log y ⇔ log(xy)

• log
`x^(n)` ⇔ n log x

• log x = log y ⇔ x = y

Given

3ln2 + ln8 = 2ln(4x)

ln 2³ + ln8 = ln(4x)²

ln8 + ln8 = ln 16x²

ln(8 × 8) = ln 16x²

ln 64 = 16x², hence

16x² = 64 ( divide both sides by 16 )

x² = 4 ( take the square root of both sides )

x =
`√(4)` = 2