ln(x+2)+ln(x-4)=ln*7

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Solution for ln(x+2)+ln(x-4)=ln*7 equation:


Simplifying
ln(x + 2) + ln(x + -4) = ln * 7

Reorder the terms:
ln(2 + x) + ln(x + -4) = ln * 7
(2 * ln + x * ln) + ln(x + -4) = ln * 7
(2ln + lnx) + ln(x + -4) = ln * 7

Reorder the terms:
2ln + lnx + ln(-4 + x) = ln * 7
2ln + lnx + (-4 * ln + x * ln) = ln * 7
2ln + lnx + (-4ln + lnx) = ln * 7

Reorder the terms:
2ln + -4ln + lnx + lnx = ln * 7

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

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

Reorder the terms for easier multiplication:
-2ln + 2lnx = 7ln

Solving
-2ln + 2lnx = 7ln

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.
-2ln + -7ln + 2lnx = 7ln + -7ln

Combine like terms: -2ln + -7ln = -9ln
-9ln + 2lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-9ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -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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