Inx In 9x 2 4SolutionGiven in question ln x lnx2 4 usin

Solution

Given in question

ln x + ln(x+2) = 4

using property ln(A) +ln (B) = ln(AB)

we get

ln (x(x+2)) =4

or

x²+2x = e⁴

x²+2x-e⁴=0

applying solution for ax² +bx +c=0

here, a=1,b=2,c=-e⁴

so

x₁=(-b+(b²-4ac)^1/2)/2a

and, x₂ =(-b-(b²-4ac)^1/2)/2a

putting above values we get

x₁=-1+(1+e⁴)^1/2

x₂=-1-(1+e⁴)^1/2

x₂ cannot be the solution as, log values cant be negative so, neglecting x₂

we get only one solution -1+(1+e⁴)^1/2

x=8.910.....ans.