2lnx-ln(2x-7)=ln(x+2)

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Solution for 2lnx-ln(2x-7)=ln(x+2) equation: 


Simplifying
2lnx + -1ln(2x + -7) = ln(x + 2)

Reorder the terms:
2lnx + -1ln(-7 + 2x) = ln(x + 2)
2lnx + (-7 * -1ln + 2x * -1ln) = ln(x + 2)
2lnx + (7ln + -2lnx) = ln(x + 2)

Reorder the terms:
7ln + 2lnx + -2lnx = ln(x + 2)

Combine like terms: 2lnx + -2lnx = 0
7ln + 0 = ln(x + 2)
7ln = ln(x + 2)

Reorder the terms:
7ln = ln(2 + x)
7ln = (2 * ln + x * ln)
7ln = (2ln + lnx)

Solving
7ln = 2ln + lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
7ln + -2ln = 2ln + -2ln + lnx

Combine like terms: 7ln + -2ln = 5ln
5ln = 2ln + -2ln + lnx

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

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

Combine like terms: lnx + -1lnx = 0
5ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -1x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

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

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

Simplifying
0 = -5 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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