ln(x-3)+ln(x+2)=ln(x-7)

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Solution for ln(x-3)+ln(x+2)=ln(x-7) equation:


Simplifying
ln(x + -3) + ln(x + 2) = ln(x + -7)

Reorder the terms:
ln(-3 + x) + ln(x + 2) = ln(x + -7)
(-3 * ln + x * ln) + ln(x + 2) = ln(x + -7)
(-3ln + lnx) + ln(x + 2) = ln(x + -7)

Reorder the terms:
-3ln + lnx + ln(2 + x) = ln(x + -7)
-3ln + lnx + (2 * ln + x * ln) = ln(x + -7)
-3ln + lnx + (2ln + lnx) = ln(x + -7)

Reorder the terms:
-3ln + 2ln + lnx + lnx = ln(x + -7)

Combine like terms: -3ln + 2ln = -1ln
-1ln + lnx + lnx = ln(x + -7)

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

Reorder the terms:
-1ln + 2lnx = ln(-7 + x)
-1ln + 2lnx = (-7 * ln + x * ln)
-1ln + 2lnx = (-7ln + lnx)

Solving
-1ln + 2lnx = -7ln + lnx

Solving for variable 'l'.

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

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

Combine like terms: -1ln + 7ln = 6ln
6ln + 2lnx = -7ln + 7ln + lnx

Combine like terms: -7ln + 7ln = 0
6ln + 2lnx = 0 + lnx
6ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
6ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
6ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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