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

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


Simplifying
ln(6x + 2) = ln(5)

Reorder the terms:
ln(2 + 6x) = ln(5)
(2 * ln + 6x * ln) = ln(5)
(2ln + 6lnx) = ln(5)

Reorder the terms for easier multiplication:
2ln + 6lnx = 5ln

Solving
2ln + 6lnx = 5ln

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.
2ln + -5ln + 6lnx = 5ln + -5ln

Combine like terms: 2ln + -5ln = -3ln
-3ln + 6lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-3ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-1 + 2x) = 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 '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Add '-2x' to each side of the equation. 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 0 = 1 + -2x Simplifying 0 = 1 + -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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