ln(x+3)=ln(5x)

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


Simplifying
ln(x + 3) = ln(5x)

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

Remove parenthesis around (5x)
3ln + lnx = ln * 5x

Reorder the terms for easier multiplication:
3ln + lnx = 5ln * x

Multiply ln * x
3ln + lnx = 5lnx

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

Combine like terms: lnx + -5lnx = -4lnx
3ln + -4lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
3ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Add '4x' to each side of the equation.
-4x + 4x = -3 + 4x

Combine like terms: -4x + 4x = 0
0 = -3 + 4x

Simplifying
0 = -3 + 4x

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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