ln(2x+5)+ln(x-8)-2lnx=0

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Solution for ln(2x+5)+ln(x-8)-2lnx=0 equation:


Simplifying
ln(2x + 5) + ln(x + -8) + -2lnx = 0

Reorder the terms:
ln(5 + 2x) + ln(x + -8) + -2lnx = 0
(5 * ln + 2x * ln) + ln(x + -8) + -2lnx = 0
(5ln + 2lnx) + ln(x + -8) + -2lnx = 0

Reorder the terms:
5ln + 2lnx + ln(-8 + x) + -2lnx = 0
5ln + 2lnx + (-8 * ln + x * ln) + -2lnx = 0
5ln + 2lnx + (-8ln + lnx) + -2lnx = 0

Reorder the terms:
5ln + -8ln + 2lnx + lnx + -2lnx = 0

Combine like terms: 5ln + -8ln = -3ln
-3ln + 2lnx + lnx + -2lnx = 0

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

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

Solving
-3ln + 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(-3 + 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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