ln(6x+2)=ln(3x-19)

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Solution for ln(6x+2)=ln(3x-19) equation:


Simplifying
ln(6x + 2) = ln(3x + -19)

Reorder the terms:
ln(2 + 6x) = ln(3x + -19)
(2 * ln + 6x * ln) = ln(3x + -19)
(2ln + 6lnx) = ln(3x + -19)

Reorder the terms:
2ln + 6lnx = ln(-19 + 3x)
2ln + 6lnx = (-19 * ln + 3x * ln)
2ln + 6lnx = (-19ln + 3lnx)

Solving
2ln + 6lnx = -19ln + 3lnx

Solving for variable 'l'.

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

Add '19ln' to each side of the equation.
2ln + 19ln + 6lnx = -19ln + 19ln + 3lnx

Combine like terms: 2ln + 19ln = 21ln
21ln + 6lnx = -19ln + 19ln + 3lnx

Combine like terms: -19ln + 19ln = 0
21ln + 6lnx = 0 + 3lnx
21ln + 6lnx = 3lnx

Add '-3lnx' to each side of the equation.
21ln + 6lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 6lnx + -3lnx = 3lnx
21ln + 3lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
21ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(7 + x) = 0

Ignore the factor 3.

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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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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