ln(4x+3)=ln(3x+5)

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Solution for ln(4x+3)=ln(3x+5) equation: 


Simplifying
ln(4x + 3) = ln(3x + 5)

Reorder the terms:
ln(3 + 4x) = ln(3x + 5)
(3 * ln + 4x * ln) = ln(3x + 5)
(3ln + 4lnx) = ln(3x + 5)

Reorder the terms:
3ln + 4lnx = ln(5 + 3x)
3ln + 4lnx = (5 * ln + 3x * ln)
3ln + 4lnx = (5ln + 3lnx)

Solving
3ln + 4lnx = 5ln + 3lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
3ln + -5ln + 4lnx = 5ln + -5ln + 3lnx

Combine like terms: 3ln + -5ln = -2ln
-2ln + 4lnx = 5ln + -5ln + 3lnx

Combine like terms: 5ln + -5ln = 0
-2ln + 4lnx = 0 + 3lnx
-2ln + 4lnx = 3lnx

Add '-3lnx' to each side of the equation.
-2ln + 4lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 4lnx + -3lnx = 1lnx
-2ln + 1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 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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