ln(x-3)-lnx=-ln(5x)

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Solution for ln(x-3)-lnx=-ln(5x) equation: 


Simplifying
ln(x + -3) + -1lnx = -1ln(5x)

Reorder the terms:
ln(-3 + x) + -1lnx = -1ln(5x)
(-3 * ln + x * ln) + -1lnx = -1ln(5x)
(-3ln + lnx) + -1lnx = -1ln(5x)

Combine like terms: lnx + -1lnx = 0
-3ln + 0 = -1ln(5x)
-3ln = -1ln(5x)

Remove parenthesis around (5x)
-3ln = -1ln * 5x

Reorder the terms for easier multiplication:
-3ln = -1 * 5ln * x

Multiply -1 * 5
-3ln = -5ln * x

Multiply ln * x
-3ln = -5lnx

Solving
-3ln = -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.
-3ln + 5lnx = -5lnx + 5lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 5x) = 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 '(-3 + 5x)' equal to zero and attempt to solve:

Simplifying
-3 + 5x = 0

Solving
-3 + 5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 5x = 0 + 3

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

Combine like terms: 0 + 3 = 3
5x = 3

Add '-5x' to each side of the equation.
5x + -5x = 3 + -5x

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

Simplifying
0 = 3 + -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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