Question

Solve the equation for x. 3 In(x) + 2 In (4)= In(128)

Answer 1

Answer:

x=2

Step-by-step explanation:

3 ln(x) + 2 ln (4)= ln(128)

a ln (b) = ln b^a

In(x^3) +  In (4^2)= In(128)

In(x^3) +  In (16)= In(128)

ln a + ln b = ln (ab)

In(16x^3) = In(128)

raise each side to the power of e

e^ In(16x^3) = e ^In(128)

e^ ln  cancels out

(16x^3) = (128)

divide by 16

(16x^3)/16 = (128)/16

x^3 = 8

take the cube root on each side

(x^3)^1/3 = 8^ 1/3

x =2