ln(x+4)=ln(2x-3)

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Solution for ln(x+4)=ln(2x-3) equation: 


Simplifying
ln(x + 4) = ln(2x + -3)

Reorder the terms:
ln(4 + x) = ln(2x + -3)
(4 * ln + x * ln) = ln(2x + -3)
(4ln + lnx) = ln(2x + -3)

Reorder the terms:
4ln + lnx = ln(-3 + 2x)
4ln + lnx = (-3 * ln + 2x * ln)
4ln + lnx = (-3ln + 2lnx)

Solving
4ln + lnx = -3ln + 2lnx

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.
4ln + 3ln + lnx = -3ln + 3ln + 2lnx

Combine like terms: 4ln + 3ln = 7ln
7ln + lnx = -3ln + 3ln + 2lnx

Combine like terms: -3ln + 3ln = 0
7ln + lnx = 0 + 2lnx
7ln + lnx = 2lnx

Add '-2lnx' to each side of the equation.
7ln + lnx + -2lnx = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
7ln + -1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
7ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Add 'x' to each side of the equation.
-1x + x = -7 + x

Combine like terms: -1x + x = 0
0 = -7 + x

Simplifying
0 = -7 + x

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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