ln(3x+1)=ln(x)

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Solution for ln(3x+1)=ln(x) equation:


Simplifying
ln(3x + 1) = ln(x)

Reorder the terms:
ln(1 + 3x) = ln(x)
(1 * ln + 3x * ln) = ln(x)
(1ln + 3lnx) = ln(x)

Multiply ln * x
1ln + 3lnx = lnx

Solving
1ln + 3lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
1ln + 3lnx + -1lnx = lnx + -1lnx

Combine like terms: 3lnx + -1lnx = 2lnx
1ln + 2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 2x) = 0

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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