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

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


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

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

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

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

Combine like terms: 2ln + -2ln = 0
0 + lnx + 3lnx = 2ln(2x)
lnx + 3lnx = 2ln(2x)

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

Remove parenthesis around (2x)
4lnx = 2ln * 2x

Reorder the terms for easier multiplication:
4lnx = 2 * 2ln * x

Multiply 2 * 2
4lnx = 4ln * x

Multiply ln * x
4lnx = 4lnx

Add '-4lnx' to each side of the equation.
4lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
0 = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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