ln(2x-1)+ln(x-5)=ln(x+9)

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Solution for ln(2x-1)+ln(x-5)=ln(x+9) equation:


Simplifying
ln(2x + -1) + ln(x + -5) = ln(x + 9)

Reorder the terms:
ln(-1 + 2x) + ln(x + -5) = ln(x + 9)
(-1 * ln + 2x * ln) + ln(x + -5) = ln(x + 9)
(-1ln + 2lnx) + ln(x + -5) = ln(x + 9)

Reorder the terms:
-1ln + 2lnx + ln(-5 + x) = ln(x + 9)
-1ln + 2lnx + (-5 * ln + x * ln) = ln(x + 9)
-1ln + 2lnx + (-5ln + lnx) = ln(x + 9)

Reorder the terms:
-1ln + -5ln + 2lnx + lnx = ln(x + 9)

Combine like terms: -1ln + -5ln = -6ln
-6ln + 2lnx + lnx = ln(x + 9)

Combine like terms: 2lnx + lnx = 3lnx
-6ln + 3lnx = ln(x + 9)

Reorder the terms:
-6ln + 3lnx = ln(9 + x)
-6ln + 3lnx = (9 * ln + x * ln)
-6ln + 3lnx = (9ln + lnx)

Solving
-6ln + 3lnx = 9ln + lnx

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
-6ln + -9ln + 3lnx = 9ln + -9ln + lnx

Combine like terms: -6ln + -9ln = -15ln
-15ln + 3lnx = 9ln + -9ln + lnx

Combine like terms: 9ln + -9ln = 0
-15ln + 3lnx = 0 + lnx
-15ln + 3lnx = lnx

Add '-1lnx' to each side of the equation.
-15ln + 3lnx + -1lnx = lnx + -1lnx

Combine like terms: 3lnx + -1lnx = 2lnx
-15ln + 2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-15ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Add '-2x' to each side of the equation. 2x + -2x = 15 + -2x Combine like terms: 2x + -2x = 0 0 = 15 + -2x Simplifying 0 = 15 + -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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