ln(5x-20)=ln(4x-12)

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Solution for ln(5x-20)=ln(4x-12) equation: 


Simplifying
ln(5x + -20) = ln(4x + -12)

Reorder the terms:
ln(-20 + 5x) = ln(4x + -12)
(-20 * ln + 5x * ln) = ln(4x + -12)
(-20ln + 5lnx) = ln(4x + -12)

Reorder the terms:
-20ln + 5lnx = ln(-12 + 4x)
-20ln + 5lnx = (-12 * ln + 4x * ln)
-20ln + 5lnx = (-12ln + 4lnx)

Solving
-20ln + 5lnx = -12ln + 4lnx

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
-20ln + 12ln + 5lnx = -12ln + 12ln + 4lnx

Combine like terms: -20ln + 12ln = -8ln
-8ln + 5lnx = -12ln + 12ln + 4lnx

Combine like terms: -12ln + 12ln = 0
-8ln + 5lnx = 0 + 4lnx
-8ln + 5lnx = 4lnx

Add '-4lnx' to each side of the equation.
-8ln + 5lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 5lnx + -4lnx = 1lnx
-8ln + 1lnx = 4lnx + -4lnx

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

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

Simplifying
-8 + x = 0

Solving
-8 + x = 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 + x = 0 + 8

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

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

Add '-1x' to each side of the equation.
x + -1x = 8 + -1x

Combine like terms: x + -1x = 0
0 = 8 + -1x

Simplifying
0 = 8 + -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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