ln(x)+(x-6)=ln(6x)

Solution for ln(x)+(x-6)=ln(6x) equation:

Simplifying
ln(x) + (x + -6) = ln(6x)

Multiply ln * x
lnx + (x + -6) = ln(6x)

Reorder the terms:
lnx + (-6 + x) = ln(6x)

Remove parenthesis around (-6 + x)
lnx + -6 + x = ln(6x)

Reorder the terms:
-6 + lnx + x = ln(6x)

Remove parenthesis around (6x)
-6 + lnx + x = ln * 6x

Reorder the terms for easier multiplication:
-6 + lnx + x = 6ln * x

Multiply ln * x
-6 + lnx + x = 6lnx

Solving
-6 + lnx + x = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
-6 + lnx + -6lnx + x = 6lnx + -6lnx

Combine like terms: lnx + -6lnx = -5lnx
-6 + -5lnx + x = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-6 + -5lnx + x = 0

Add '6' to each side of the equation.
-6 + -5lnx + 6 + x = 0 + 6

Reorder the terms:
-6 + 6 + -5lnx + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5lnx + x = 0 + 6
-5lnx + x = 0 + 6

Combine like terms: 0 + 6 = 6
-5lnx + x = 6

Add '-1x' to each side of the equation.
-5lnx + x + -1x = 6 + -1x

Combine like terms: x + -1x = 0
-5lnx + 0 = 6 + -1x
-5lnx = 6 + -1x

Divide each side by '-5nx'.
l = -1.2n-1x-1 + 0.2n-1

Simplifying
l = -1.2n-1x-1 + 0.2n-1

Reorder the terms:
l = 0.2n-1 + -1.2n-1x-1