ln(2x)=ln(x+3)

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


Simplifying
ln(2x) = ln(x + 3)

Remove parenthesis around (2x)
ln * 2x = ln(x + 3)

Reorder the terms for easier multiplication:
2ln * x = ln(x + 3)

Multiply ln * x
2lnx = ln(x + 3)

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

Solving
2lnx = 3ln + lnx

Solving for variable 'l'.

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

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

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

Add '-1lnx' to each side of the equation.
-3ln + 2lnx + -1lnx = lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
-3ln + 1lnx = 0

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