ln(5x-4)=ln(16)-ln(x-4)

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Solution for ln(5x-4)=ln(16)-ln(x-4) equation:


Simplifying
ln(5x + -4) = ln(16) + -1ln(x + -4)

Reorder the terms:
ln(-4 + 5x) = ln(16) + -1ln(x + -4)
(-4 * ln + 5x * ln) = ln(16) + -1ln(x + -4)
(-4ln + 5lnx) = ln(16) + -1ln(x + -4)

Reorder the terms for easier multiplication:
-4ln + 5lnx = 16ln + -1ln(x + -4)

Reorder the terms:
-4ln + 5lnx = 16ln + -1ln(-4 + x)
-4ln + 5lnx = 16ln + (-4 * -1ln + x * -1ln)
-4ln + 5lnx = 16ln + (4ln + -1lnx)

Combine like terms: 16ln + 4ln = 20ln
-4ln + 5lnx = 20ln + -1lnx

Solving
-4ln + 5lnx = 20ln + -1lnx

Solving for variable 'l'.

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

Add '-20ln' to each side of the equation.
-4ln + -20ln + 5lnx = 20ln + -20ln + -1lnx

Combine like terms: -4ln + -20ln = -24ln
-24ln + 5lnx = 20ln + -20ln + -1lnx

Combine like terms: 20ln + -20ln = 0
-24ln + 5lnx = 0 + -1lnx
-24ln + 5lnx = -1lnx

Add 'lnx' to each side of the equation.
-24ln + 5lnx + lnx = -1lnx + lnx

Combine like terms: 5lnx + lnx = 6lnx
-24ln + 6lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-24ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '6ln'.
6ln(-4 + x) = 0

Ignore the factor 6.

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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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