ln(x)+ln(x-3e)=ln(4)+2

Solution for ln(x)+ln(x-3e)=ln(4)+2 equation:

Simplifying
ln(x) + ln(x + -3e) = ln(4) + 2

Multiply ln * x
lnx + ln(x + -3e) = ln(4) + 2

Reorder the terms:
lnx + ln(-3e + x) = ln(4) + 2
lnx + (-3e * ln + x * ln) = ln(4) + 2
lnx + (-3eln + lnx) = ln(4) + 2

Reorder the terms:
-3eln + lnx + lnx = ln(4) + 2

Combine like terms: lnx + lnx = 2lnx
-3eln + 2lnx = ln(4) + 2

Reorder the terms for easier multiplication:
-3eln + 2lnx = 4ln + 2

Reorder the terms:
-3eln + 2lnx = 2 + 4ln

Solving
-3eln + 2lnx = 2 + 4ln

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Add '-2lnx' to each side of the equation.
-3eln + 2lnx + -2lnx = 2 + 4ln + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-3eln + 0 = 2 + 4ln + -2lnx
-3eln = 2 + 4ln + -2lnx

Divide each side by '-3ln'.
e = -0.6666666667l-1n-1 + -1.333333333 + 0.6666666667x

Simplifying
e = -0.6666666667l-1n-1 + -1.333333333 + 0.6666666667x

Reorder the terms:
e = -1.333333333 + -0.6666666667l-1n-1 + 0.6666666667x