ln(2x-5)=ln(x-1)

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Solution for ln(2x-5)=ln(x-1) equation:


Simplifying
ln(2x + -5) = ln(x + -1)

Reorder the terms:
ln(-5 + 2x) = ln(x + -1)
(-5 * ln + 2x * ln) = ln(x + -1)
(-5ln + 2lnx) = ln(x + -1)

Reorder the terms:
-5ln + 2lnx = ln(-1 + x)
-5ln + 2lnx = (-1 * ln + x * ln)
-5ln + 2lnx = (-1ln + lnx)

Solving
-5ln + 2lnx = -1ln + lnx

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
-5ln + ln + 2lnx = -1ln + ln + lnx

Combine like terms: -5ln + ln = -4ln
-4ln + 2lnx = -1ln + ln + lnx

Combine like terms: -1ln + ln = 0
-4ln + 2lnx = 0 + lnx
-4ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-4ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-4ln + 1lnx = lnx + -1lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 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 '(-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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