ln(x)-ln(3)=ln(4)-ln(x+4)

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Solution for ln(x)-ln(3)=ln(4)-ln(x+4) equation:


Simplifying
ln(x) + -1ln(3) = ln(4) + -1ln(x + 4)

Multiply ln * x
lnx + -1ln(3) = ln(4) + -1ln(x + 4)

Reorder the terms for easier multiplication:
lnx + -1 * 3ln = ln(4) + -1ln(x + 4)

Multiply -1 * 3
lnx + -3ln = ln(4) + -1ln(x + 4)

Reorder the terms:
-3ln + lnx = ln(4) + -1ln(x + 4)

Reorder the terms for easier multiplication:
-3ln + lnx = 4ln + -1ln(x + 4)

Reorder the terms:
-3ln + lnx = 4ln + -1ln(4 + x)
-3ln + lnx = 4ln + (4 * -1ln + x * -1ln)
-3ln + lnx = 4ln + (-4ln + -1lnx)

Combine like terms: 4ln + -4ln = 0
-3ln + lnx = 0 + -1lnx
-3ln + lnx = -1lnx

Solving
-3ln + lnx = -1lnx

Solving for variable 'l'.

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

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

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

Combine like terms: -1lnx + lnx = 0
-3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 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 '(-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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