Ln(5x)-ln(x+2)=ln(3)

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Solution for Ln(5x)-ln(x+2)=ln(3) equation: 


Simplifying
Ln(5x) + -1ln(x + 2) = ln(3)

Remove parenthesis around (5x)
nL * 5x + -1ln(x + 2) = ln(3)

Reorder the terms for easier multiplication:
5nL * x + -1ln(x + 2) = ln(3)

Multiply nL * x
5nxL + -1ln(x + 2) = ln(3)

Reorder the terms:
5nxL + -1ln(2 + x) = ln(3)
5nxL + (2 * -1ln + x * -1ln) = ln(3)
5nxL + (-2ln + -1lnx) = ln(3)

Reorder the terms:
-2ln + -1lnx + 5nxL = ln(3)

Reorder the terms for easier multiplication:
-2ln + -1lnx + 5nxL = 3ln

Solving
-2ln + -1lnx + 5nxL = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-2ln + -1lnx + -3ln + 5nxL = 3ln + -3ln

Reorder the terms:
-2ln + -3ln + -1lnx + 5nxL = 3ln + -3ln

Combine like terms: -2ln + -3ln = -5ln
-5ln + -1lnx + 5nxL = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-5ln + -1lnx + 5nxL = 0

Add '-5nxL' to each side of the equation.
-5ln + -1lnx + 5nxL + -5nxL = 0 + -5nxL

Combine like terms: 5nxL + -5nxL = 0
-5ln + -1lnx + 0 = 0 + -5nxL
-5ln + -1lnx = 0 + -5nxL
Remove the zero:
-5ln + -1lnx = -5nxL

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + -1lx + 5xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-5l + -1lx + 5xL)' equal to zero and attempt to solve:

Simplifying
-5l + -1lx + 5xL = 0

Solving
-5l + -1lx + 5xL = 0

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

Add '-5xL' to each side of the equation.
-5l + -1lx + 5xL + -5xL = 0 + -5xL

Combine like terms: 5xL + -5xL = 0
-5l + -1lx + 0 = 0 + -5xL
-5l + -1lx = 0 + -5xL
Remove the zero:
-5l + -1lx = -5xL

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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