ln(5x)=ln(4x+2)

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Solution for ln(5x)=ln(4x+2) equation: 


Simplifying
ln(5x) = ln(4x + 2)

Remove parenthesis around (5x)
ln * 5x = ln(4x + 2)

Reorder the terms for easier multiplication:
5ln * x = ln(4x + 2)

Multiply ln * x
5lnx = ln(4x + 2)

Reorder the terms:
5lnx = ln(2 + 4x)
5lnx = (2 * ln + 4x * ln)
5lnx = (2ln + 4lnx)

Solving
5lnx = 2ln + 4lnx

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.
-2ln + 5lnx = 2ln + -2ln + 4lnx

Combine like terms: 2ln + -2ln = 0
-2ln + 5lnx = 0 + 4lnx
-2ln + 5lnx = 4lnx

Add '-4lnx' to each side of the equation.
-2ln + 5lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 5lnx + -4lnx = 1lnx
-2ln + 1lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-2ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Add '-1x' to each side of the equation.
x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
0 = 2 + -1x

Simplifying
0 = 2 + -1x

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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