(4x-9)ln(5)=(x-4)ln(5)

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Solution for (4x-9)ln(5)=(x-4)ln(5) equation:


Simplifying
(4x + -9) * ln(5) = (x + -4) * ln(5)

Reorder the terms:
(-9 + 4x) * ln(5) = (x + -4) * ln(5)

Reorder the terms for easier multiplication:
5ln(-9 + 4x) = (x + -4) * ln(5)
(-9 * 5ln + 4x * 5ln) = (x + -4) * ln(5)
(-45ln + 20lnx) = (x + -4) * ln(5)

Reorder the terms:
-45ln + 20lnx = (-4 + x) * ln(5)

Reorder the terms for easier multiplication:
-45ln + 20lnx = 5ln(-4 + x)
-45ln + 20lnx = (-4 * 5ln + x * 5ln)
-45ln + 20lnx = (-20ln + 5lnx)

Solving
-45ln + 20lnx = -20ln + 5lnx

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.
-45ln + 20ln + 20lnx = -20ln + 20ln + 5lnx

Combine like terms: -45ln + 20ln = -25ln
-25ln + 20lnx = -20ln + 20ln + 5lnx

Combine like terms: -20ln + 20ln = 0
-25ln + 20lnx = 0 + 5lnx
-25ln + 20lnx = 5lnx

Add '-5lnx' to each side of the equation.
-25ln + 20lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 20lnx + -5lnx = 15lnx
-25ln + 15lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-25ln + 15lnx = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(-5 + 3x) = 0

Ignore the factor 5.

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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -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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