ln(21)-lnx=ln(x-4)

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Solution for ln(21)-lnx=ln(x-4) equation: 


Simplifying
ln(21) + -1lnx = ln(x + -4)

Reorder the terms for easier multiplication:
21ln + -1lnx = ln(x + -4)

Reorder the terms:
21ln + -1lnx = ln(-4 + x)
21ln + -1lnx = (-4 * ln + x * ln)
21ln + -1lnx = (-4ln + lnx)

Solving
21ln + -1lnx = -4ln + lnx

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
21ln + 4ln + -1lnx = -4ln + 4ln + lnx

Combine like terms: 21ln + 4ln = 25ln
25ln + -1lnx = -4ln + 4ln + lnx

Combine like terms: -4ln + 4ln = 0
25ln + -1lnx = 0 + lnx
25ln + -1lnx = lnx

Add '-1lnx' to each side of the equation.
25ln + -1lnx + -1lnx = lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
25ln + -2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
25ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(25 + -2x) = 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 '(25 + -2x)' equal to zero and attempt to solve:

Simplifying
25 + -2x = 0

Solving
25 + -2x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2x = 0 + -25
-2x = 0 + -25

Combine like terms: 0 + -25 = -25
-2x = -25

Add '2x' to each side of the equation.
-2x + 2x = -25 + 2x

Combine like terms: -2x + 2x = 0
0 = -25 + 2x

Simplifying
0 = -25 + 2x

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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