ln(x+4)+ln(x)=ln(x+18)

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Solution for ln(x+4)+ln(x)=ln(x+18) equation:


Simplifying
ln(x + 4) + ln(x) = ln(x + 18)

Reorder the terms:
ln(4 + x) + ln(x) = ln(x + 18)
(4 * ln + x * ln) + ln(x) = ln(x + 18)
(4ln + lnx) + ln(x) = ln(x + 18)

Multiply ln * x
4ln + lnx + lnx = ln(x + 18)

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(x + 18)

Reorder the terms:
4ln + 2lnx = ln(18 + x)
4ln + 2lnx = (18 * ln + x * ln)
4ln + 2lnx = (18ln + lnx)

Solving
4ln + 2lnx = 18ln + lnx

Solving for variable 'l'.

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

Add '-18ln' to each side of the equation.
4ln + -18ln + 2lnx = 18ln + -18ln + lnx

Combine like terms: 4ln + -18ln = -14ln
-14ln + 2lnx = 18ln + -18ln + lnx

Combine like terms: 18ln + -18ln = 0
-14ln + 2lnx = 0 + lnx
-14ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-14ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-14ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-14ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-14 + 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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -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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