ln(x+1)+ln(x+4)=ln(x+9)

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Solution for ln(x+1)+ln(x+4)=ln(x+9) equation:


Simplifying
ln(x + 1) + ln(x + 4) = ln(x + 9)

Reorder the terms:
ln(1 + x) + ln(x + 4) = ln(x + 9)
(1 * ln + x * ln) + ln(x + 4) = ln(x + 9)
(1ln + lnx) + ln(x + 4) = ln(x + 9)

Reorder the terms:
1ln + lnx + ln(4 + x) = ln(x + 9)
1ln + lnx + (4 * ln + x * ln) = ln(x + 9)
1ln + lnx + (4ln + lnx) = ln(x + 9)

Reorder the terms:
1ln + 4ln + lnx + lnx = ln(x + 9)

Combine like terms: 1ln + 4ln = 5ln
5ln + lnx + lnx = ln(x + 9)

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

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

Solving
5ln + 2lnx = 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.
5ln + -9ln + 2lnx = 9ln + -9ln + lnx

Combine like terms: 5ln + -9ln = -4ln
-4ln + 2lnx = 9ln + -9ln + lnx

Combine like terms: 9ln + -9ln = 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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