ln(x-20)+ln(x-3)=ln(108+3x^2+5x)

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Solution for ln(x-20)+ln(x-3)=ln(108+3x^2+5x) equation:


Simplifying
ln(x + -20) + ln(x + -3) = ln(108 + 3x2 + 5x)

Reorder the terms:
ln(-20 + x) + ln(x + -3) = ln(108 + 3x2 + 5x)
(-20 * ln + x * ln) + ln(x + -3) = ln(108 + 3x2 + 5x)
(-20ln + lnx) + ln(x + -3) = ln(108 + 3x2 + 5x)

Reorder the terms:
-20ln + lnx + ln(-3 + x) = ln(108 + 3x2 + 5x)
-20ln + lnx + (-3 * ln + x * ln) = ln(108 + 3x2 + 5x)
-20ln + lnx + (-3ln + lnx) = ln(108 + 3x2 + 5x)

Reorder the terms:
-20ln + -3ln + lnx + lnx = ln(108 + 3x2 + 5x)

Combine like terms: -20ln + -3ln = -23ln
-23ln + lnx + lnx = ln(108 + 3x2 + 5x)

Combine like terms: lnx + lnx = 2lnx
-23ln + 2lnx = ln(108 + 3x2 + 5x)

Reorder the terms:
-23ln + 2lnx = ln(108 + 5x + 3x2)
-23ln + 2lnx = (108 * ln + 5x * ln + 3x2 * ln)
-23ln + 2lnx = (108ln + 5lnx + 3lnx2)

Solving
-23ln + 2lnx = 108ln + 5lnx + 3lnx2

Solving for variable 'l'.

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

Add '-108ln' to each side of the equation.
-23ln + -108ln + 2lnx = 108ln + 5lnx + -108ln + 3lnx2

Combine like terms: -23ln + -108ln = -131ln
-131ln + 2lnx = 108ln + 5lnx + -108ln + 3lnx2

Reorder the terms:
-131ln + 2lnx = 108ln + -108ln + 5lnx + 3lnx2

Combine like terms: 108ln + -108ln = 0
-131ln + 2lnx = 0 + 5lnx + 3lnx2
-131ln + 2lnx = 5lnx + 3lnx2

Add '-5lnx' to each side of the equation.
-131ln + 2lnx + -5lnx = 5lnx + -5lnx + 3lnx2

Combine like terms: 2lnx + -5lnx = -3lnx
-131ln + -3lnx = 5lnx + -5lnx + 3lnx2

Combine like terms: 5lnx + -5lnx = 0
-131ln + -3lnx = 0 + 3lnx2
-131ln + -3lnx = 3lnx2

Add '-3lnx2' to each side of the equation.
-131ln + -3lnx + -3lnx2 = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
-131ln + -3lnx + -3lnx2 = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(131 + 3x + 3x2) = 0

Ignore the factor -1.

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 '(131 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 131 + 3x + 3x2 = 0 Solving 131 + 3x + 3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-131' to each side of the equation. 131 + 3x + -131 + 3x2 = 0 + -131 Reorder the terms: 131 + -131 + 3x + 3x2 = 0 + -131 Combine like terms: 131 + -131 = 0 0 + 3x + 3x2 = 0 + -131 3x + 3x2 = 0 + -131 Combine like terms: 0 + -131 = -131 3x + 3x2 = -131 Add '-3x' to each side of the equation. 3x + -3x + 3x2 = -131 + -3x Combine like terms: 3x + -3x = 0 0 + 3x2 = -131 + -3x 3x2 = -131 + -3x Add '-3x2' to each side of the equation. 3x2 + -3x2 = -131 + -3x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = -131 + -3x + -3x2 Simplifying 0 = -131 + -3x + -3x2 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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