ln(-3x-3)=ln(2x+10)

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Solution for ln(-3x-3)=ln(2x+10) equation:


Simplifying
ln(-3x + -3) = ln(2x + 10)

Reorder the terms:
ln(-3 + -3x) = ln(2x + 10)
(-3 * ln + -3x * ln) = ln(2x + 10)
(-3ln + -3lnx) = ln(2x + 10)

Reorder the terms:
-3ln + -3lnx = ln(10 + 2x)
-3ln + -3lnx = (10 * ln + 2x * ln)
-3ln + -3lnx = (10ln + 2lnx)

Solving
-3ln + -3lnx = 10ln + 2lnx

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-3ln + -10ln + -3lnx = 10ln + -10ln + 2lnx

Combine like terms: -3ln + -10ln = -13ln
-13ln + -3lnx = 10ln + -10ln + 2lnx

Combine like terms: 10ln + -10ln = 0
-13ln + -3lnx = 0 + 2lnx
-13ln + -3lnx = 2lnx

Add '-2lnx' to each side of the equation.
-13ln + -3lnx + -2lnx = 2lnx + -2lnx

Combine like terms: -3lnx + -2lnx = -5lnx
-13ln + -5lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-13ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(13 + 5x) = 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 '(13 + 5x)' equal to zero and attempt to solve: Simplifying 13 + 5x = 0 Solving 13 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 5x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5x = 0 + -13 5x = 0 + -13 Combine like terms: 0 + -13 = -13 5x = -13 Add '-5x' to each side of the equation. 5x + -5x = -13 + -5x Combine like terms: 5x + -5x = 0 0 = -13 + -5x Simplifying 0 = -13 + -5x 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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