2ln(x-1)+ln(6x+9)=2ln(2x+3)

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Solution for 2ln(x-1)+ln(6x+9)=2ln(2x+3) equation:


Simplifying
2ln(x + -1) + ln(6x + 9) = 2ln(2x + 3)

Reorder the terms:
2ln(-1 + x) + ln(6x + 9) = 2ln(2x + 3)
(-1 * 2ln + x * 2ln) + ln(6x + 9) = 2ln(2x + 3)
(-2ln + 2lnx) + ln(6x + 9) = 2ln(2x + 3)

Reorder the terms:
-2ln + 2lnx + ln(9 + 6x) = 2ln(2x + 3)
-2ln + 2lnx + (9 * ln + 6x * ln) = 2ln(2x + 3)
-2ln + 2lnx + (9ln + 6lnx) = 2ln(2x + 3)

Reorder the terms:
-2ln + 9ln + 2lnx + 6lnx = 2ln(2x + 3)

Combine like terms: -2ln + 9ln = 7ln
7ln + 2lnx + 6lnx = 2ln(2x + 3)

Combine like terms: 2lnx + 6lnx = 8lnx
7ln + 8lnx = 2ln(2x + 3)

Reorder the terms:
7ln + 8lnx = 2ln(3 + 2x)
7ln + 8lnx = (3 * 2ln + 2x * 2ln)
7ln + 8lnx = (6ln + 4lnx)

Solving
7ln + 8lnx = 6ln + 4lnx

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
7ln + -6ln + 8lnx = 6ln + -6ln + 4lnx

Combine like terms: 7ln + -6ln = 1ln
1ln + 8lnx = 6ln + -6ln + 4lnx

Combine like terms: 6ln + -6ln = 0
1ln + 8lnx = 0 + 4lnx
1ln + 8lnx = 4lnx

Add '-4lnx' to each side of the equation.
1ln + 8lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 8lnx + -4lnx = 4lnx
1ln + 4lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
1ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Add '-4x' to each side of the equation. 4x + -4x = -1 + -4x Combine like terms: 4x + -4x = 0 0 = -1 + -4x Simplifying 0 = -1 + -4x 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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