ln(2x)+ln(x-7)-2ln(x-4)=0

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Solution for ln(2x)+ln(x-7)-2ln(x-4)=0 equation:


Simplifying
ln(2x) + ln(x + -7) + -2ln(x + -4) = 0

Remove parenthesis around (2x)
ln * 2x + ln(x + -7) + -2ln(x + -4) = 0

Reorder the terms for easier multiplication:
2ln * x + ln(x + -7) + -2ln(x + -4) = 0

Multiply ln * x
2lnx + ln(x + -7) + -2ln(x + -4) = 0

Reorder the terms:
2lnx + ln(-7 + x) + -2ln(x + -4) = 0
2lnx + (-7 * ln + x * ln) + -2ln(x + -4) = 0
2lnx + (-7ln + lnx) + -2ln(x + -4) = 0

Reorder the terms:
2lnx + -7ln + lnx + -2ln(-4 + x) = 0
2lnx + -7ln + lnx + (-4 * -2ln + x * -2ln) = 0
2lnx + -7ln + lnx + (8ln + -2lnx) = 0

Reorder the terms:
-7ln + 8ln + 2lnx + lnx + -2lnx = 0

Combine like terms: -7ln + 8ln = 1ln
1ln + 2lnx + lnx + -2lnx = 0

Combine like terms: 2lnx + lnx = 3lnx
1ln + 3lnx + -2lnx = 0

Combine like terms: 3lnx + -2lnx = 1lnx
1ln + 1lnx = 0

Solving
1ln + 1lnx = 0

Solving for variable 'l'.

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

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