ln(5*x+2)-ln(3-x)=ln*7

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Solution for ln(5*x+2)-ln(3-x)=ln*7 equation:


Simplifying
ln(5x + 2) + -1ln(3 + -1x) = ln * 7

Reorder the terms:
ln(2 + 5x) + -1ln(3 + -1x) = ln * 7
(2 * ln + 5x * ln) + -1ln(3 + -1x) = ln * 7
(2ln + 5lnx) + -1ln(3 + -1x) = ln * 7
2ln + 5lnx + (3 * -1ln + -1x * -1ln) = ln * 7
2ln + 5lnx + (-3ln + 1lnx) = ln * 7

Reorder the terms:
2ln + -3ln + 5lnx + 1lnx = ln * 7

Combine like terms: 2ln + -3ln = -1ln
-1ln + 5lnx + 1lnx = ln * 7

Combine like terms: 5lnx + 1lnx = 6lnx
-1ln + 6lnx = ln * 7

Reorder the terms for easier multiplication:
-1ln + 6lnx = 7ln

Solving
-1ln + 6lnx = 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.
-1ln + -7ln + 6lnx = 7ln + -7ln

Combine like terms: -1ln + -7ln = -8ln
-8ln + 6lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-8ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-4 + 3x) = 0

Ignore the factor 2.

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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -3x 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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