ln(5x)=ln(x+12)

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Solution for ln(5x)=ln(x+12) equation:


Simplifying
ln(5x) = ln(x + 12)

Remove parenthesis around (5x)
ln * 5x = ln(x + 12)

Reorder the terms for easier multiplication:
5ln * x = ln(x + 12)

Multiply ln * x
5lnx = ln(x + 12)

Reorder the terms:
5lnx = ln(12 + x)
5lnx = (12 * ln + x * ln)
5lnx = (12ln + lnx)

Solving
5lnx = 12ln + lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
-12ln + 5lnx = 12ln + -12ln + lnx

Combine like terms: 12ln + -12ln = 0
-12ln + 5lnx = 0 + lnx
-12ln + 5lnx = lnx

Add '-1lnx' to each side of the equation.
-12ln + 5lnx + -1lnx = lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
-12ln + 4lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-12ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(-3 + x) = 0

Ignore the factor 4.

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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