ln(3x-5)=ln(25)-ln(x-5)

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Solution for ln(3x-5)=ln(25)-ln(x-5) equation:


Simplifying
ln(3x + -5) = ln(25) + -1ln(x + -5)

Reorder the terms:
ln(-5 + 3x) = ln(25) + -1ln(x + -5)
(-5 * ln + 3x * ln) = ln(25) + -1ln(x + -5)
(-5ln + 3lnx) = ln(25) + -1ln(x + -5)

Reorder the terms for easier multiplication:
-5ln + 3lnx = 25ln + -1ln(x + -5)

Reorder the terms:
-5ln + 3lnx = 25ln + -1ln(-5 + x)
-5ln + 3lnx = 25ln + (-5 * -1ln + x * -1ln)
-5ln + 3lnx = 25ln + (5ln + -1lnx)

Combine like terms: 25ln + 5ln = 30ln
-5ln + 3lnx = 30ln + -1lnx

Solving
-5ln + 3lnx = 30ln + -1lnx

Solving for variable 'l'.

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

Add '-30ln' to each side of the equation.
-5ln + -30ln + 3lnx = 30ln + -30ln + -1lnx

Combine like terms: -5ln + -30ln = -35ln
-35ln + 3lnx = 30ln + -30ln + -1lnx

Combine like terms: 30ln + -30ln = 0
-35ln + 3lnx = 0 + -1lnx
-35ln + 3lnx = -1lnx

Add 'lnx' to each side of the equation.
-35ln + 3lnx + lnx = -1lnx + lnx

Combine like terms: 3lnx + lnx = 4lnx
-35ln + 4lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-35ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-35 + 4x) = 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 '(-35 + 4x)' equal to zero and attempt to solve: Simplifying -35 + 4x = 0 Solving -35 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + 4x = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 4x = 0 + 35 4x = 0 + 35 Combine like terms: 0 + 35 = 35 4x = 35 Add '-4x' to each side of the equation. 4x + -4x = 35 + -4x Combine like terms: 4x + -4x = 0 0 = 35 + -4x Simplifying 0 = 35 + -4x 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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