ln(4x-7)=ln(x+1)

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Solution for ln(4x-7)=ln(x+1) equation: 


Simplifying
ln(4x + -7) = ln(x + 1)

Reorder the terms:
ln(-7 + 4x) = ln(x + 1)
(-7 * ln + 4x * ln) = ln(x + 1)
(-7ln + 4lnx) = ln(x + 1)

Reorder the terms:
-7ln + 4lnx = ln(1 + x)
-7ln + 4lnx = (1 * ln + x * ln)
-7ln + 4lnx = (1ln + lnx)

Solving
-7ln + 4lnx = 1ln + lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-7ln + -1ln + 4lnx = 1ln + -1ln + lnx

Combine like terms: -7ln + -1ln = -8ln
-8ln + 4lnx = 1ln + -1ln + lnx

Combine like terms: 1ln + -1ln = 0
-8ln + 4lnx = 0 + lnx
-8ln + 4lnx = lnx

Add '-1lnx' to each side of the equation.
-8ln + 4lnx + -1lnx = lnx + -1lnx

Combine like terms: 4lnx + -1lnx = 3lnx
-8ln + 3lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-8ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + 3x) = 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 '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Add '-3x' to each side of the equation.
3x + -3x = 8 + -3x

Combine like terms: 3x + -3x = 0
0 = 8 + -3x

Simplifying
0 = 8 + -3x

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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