ln(x+5)=ln(3x-5)

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


Simplifying
ln(x + 5) = ln(3x + -5)

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

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

Solving
5ln + lnx = -5ln + 3lnx

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.
5ln + 5ln + lnx = -5ln + 5ln + 3lnx

Combine like terms: 5ln + 5ln = 10ln
10ln + lnx = -5ln + 5ln + 3lnx

Combine like terms: -5ln + 5ln = 0
10ln + lnx = 0 + 3lnx
10ln + lnx = 3lnx

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

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

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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