ln(2x+2)=ln(6x+2)-ln(x)

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Solution for ln(2x+2)=ln(6x+2)-ln(x) equation:


Simplifying
ln(2x + 2) = ln(6x + 2) + -1ln(x)

Reorder the terms:
ln(2 + 2x) = ln(6x + 2) + -1ln(x)
(2 * ln + 2x * ln) = ln(6x + 2) + -1ln(x)
(2ln + 2lnx) = ln(6x + 2) + -1ln(x)

Reorder the terms:
2ln + 2lnx = ln(2 + 6x) + -1ln(x)
2ln + 2lnx = (2 * ln + 6x * ln) + -1ln(x)
2ln + 2lnx = (2ln + 6lnx) + -1ln(x)

Multiply ln * x
2ln + 2lnx = 2ln + 6lnx + -1lnx

Combine like terms: 6lnx + -1lnx = 5lnx
2ln + 2lnx = 2ln + 5lnx

Add '-2ln' to each side of the equation.
2ln + -2ln + 2lnx = 2ln + -2ln + 5lnx

Combine like terms: 2ln + -2ln = 0
0 + 2lnx = 2ln + -2ln + 5lnx
2lnx = 2ln + -2ln + 5lnx

Combine like terms: 2ln + -2ln = 0
2lnx = 0 + 5lnx
2lnx = 5lnx

Solving
2lnx = 5lnx

Solving for variable 'l'.

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

Add '-5lnx' to each side of the equation.
2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
-3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-3lnx = 0

Divide each side by '-3'.
lnx = 0

Simplifying
lnx = 0

The solution to this equation could not be determined.

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