How do you solve lnx + ln(x+4) = 6?

1 Answer
Oct 29, 2015

-2+-sqrt(4+e^6)

Explanation:

Start of by rewriting the left hand side using properties of logarithms

ln(x(x+4))=6

Distribute the x

ln(x^2+4x)=6

Rewrite both sides in terms of the base e

e^(ln(x^2+4x))=e^6

Rewrite left hand side using properties of logarithms

x^2+4x=e^6

Substract e^6 form both sides

x^2+4x-e^6=0

Applying the quadratic formula

(-4+-sqrt(4^2-4(1)(e^6)))/(2(1))

(-4+-sqrt(16+4e^6))/2

(-4+-sqrt(4(4+e^6)))/2

(-4+-sqrt(4)sqrt(4+e^6))/2

(-4+-2sqrt(4+e^6))/2

-2+-sqrt(4+e^6)