ln(2x+5)=ln(6x-1)

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Solution for ln(2x+5)=ln(6x-1) equation:


Simplifying
ln(2x + 5) = ln(6x + -1)
Reorder the terms:
ln(5 + 2x) = ln(6x + -1)
(5 * ln + 2x * ln) = ln(6x + -1)
(5ln + 2lnx) = ln(6x + -1)
Reorder the terms:
5ln + 2lnx = ln(-1 + 6x)
5ln + 2lnx = (-1 * ln + 6x * ln)
5ln + 2lnx = (-1ln + 6lnx)
Solving
5ln + 2lnx = -1ln + 6lnx
Solving for variable 'l'.
Move all terms containing l to the left, all other terms to the right.
Add 'ln' to each side of the equation.
5ln + ln + 2lnx = -1ln + ln + 6lnx
Combine like terms: 5ln + ln = 6ln
6ln + 2lnx = -1ln + ln + 6lnx
Combine like terms: -1ln + ln = 0
6ln + 2lnx = 0 + 6lnx
6ln + 2lnx = 6lnx
Add '-6lnx' to each side of the equation.
6ln + 2lnx + -6lnx = 6lnx + -6lnx
Combine like terms: 2lnx + -6lnx = -4lnx
6ln + -4lnx = 6lnx + -6lnx
Combine like terms: 6lnx + -6lnx = 0
6ln + -4lnx = 0
Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(3 + -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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 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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