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

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


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

Reorder the terms:
2ln(-2 + x) = ln(7x)
(-2 * 2ln + x * 2ln) = ln(7x)
(-4ln + 2lnx) = ln(7x)

Remove parenthesis around (7x)
-4ln + 2lnx = ln * 7x

Reorder the terms for easier multiplication:
-4ln + 2lnx = 7ln * x

Multiply ln * x
-4ln + 2lnx = 7lnx

Solving
-4ln + 2lnx = 7lnx

Solving for variable 'l'.

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

Add '-7lnx' to each side of the equation.
-4ln + 2lnx + -7lnx = 7lnx + -7lnx

Combine like terms: 2lnx + -7lnx = -5lnx
-4ln + -5lnx = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
-4ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(4 + 5x) = 0

Ignore the factor -1.

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 '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Add '-5x' to each side of the equation.
5x + -5x = -4 + -5x

Combine like terms: 5x + -5x = 0
0 = -4 + -5x

Simplifying
0 = -4 + -5x

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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