ln(x-4)+lnx=ln(x+3)

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Solution for ln(x-4)+lnx=ln(x+3) equation:


Simplifying
ln(x + -4) + lnx = ln(x + 3)

Reorder the terms:
ln(-4 + x) + lnx = ln(x + 3)
(-4 * ln + x * ln) + lnx = ln(x + 3)
(-4ln + lnx) + lnx = ln(x + 3)

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx = ln(x + 3)

Reorder the terms:
-4ln + 2lnx = ln(3 + x)
-4ln + 2lnx = (3 * ln + x * ln)
-4ln + 2lnx = (3ln + lnx)

Solving
-4ln + 2lnx = 3ln + lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-4ln + -3ln + 2lnx = 3ln + -3ln + lnx

Combine like terms: -4ln + -3ln = -7ln
-7ln + 2lnx = 3ln + -3ln + lnx

Combine like terms: 3ln + -3ln = 0
-7ln + 2lnx = 0 + lnx
-7ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-7ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-7ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-7ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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