ln(3-2x)-(2lnx)=ln(5)

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Solution for ln(3-2x)-(2lnx)=ln(5) equation:


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

Remove parenthesis around (2lnx)
3ln + -2lnx + -1 * 2lnx = ln(5)

Multiply -1 * 2
3ln + -2lnx + -2lnx = ln(5)

Combine like terms: -2lnx + -2lnx = -4lnx
3ln + -4lnx = ln(5)

Reorder the terms for easier multiplication:
3ln + -4lnx = 5ln

Solving
3ln + -4lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
3ln + -5ln + -4lnx = 5ln + -5ln

Combine like terms: 3ln + -5ln = -2ln
-2ln + -4lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-2ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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