Solve for x given that lnxlnx2ln8 a x2x4 b x2x4 c x4 d x2 e

Solve for x, given that ln(x)+ln(x+2)=ln(8).

a) x=2,x=4

b) x=2,x=4

c) x=4

d) x=2

e) x=2,x=4

f) None of the above.

Solution

ln(x ) + ln(x +2) = ln 8

use the log property : lnA +lnB = ln(A*B)

So, ln(x(x+2) = ln8

euqte the arguments:

x(x+2) = 8

x^2 +2x -8 =0

x^2 +4x -2x -8 =0

x(x+4) -2(x+4) =0

(x-2)(x+4) =0

x = 2 , -4

Option b