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

x = 2

Step-by-step explanation:

Using the rules of logarithms

• log x + log y ⇔ log(xy)

• log ⇔ 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 = = 2