ln(x)+ln(x-3)=ln(15-x)

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Solution for ln(x)+ln(x-3)=ln(15-x) equation:


Simplifying
ln(x) + ln(x + -3) = ln(15 + -1x)

Multiply ln * x
lnx + ln(x + -3) = ln(15 + -1x)

Reorder the terms:
lnx + ln(-3 + x) = ln(15 + -1x)
lnx + (-3 * ln + x * ln) = ln(15 + -1x)
lnx + (-3ln + lnx) = ln(15 + -1x)

Reorder the terms:
-3ln + lnx + lnx = ln(15 + -1x)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(15 + -1x)
-3ln + 2lnx = (15 * ln + -1x * ln)
-3ln + 2lnx = (15ln + -1lnx)

Solving
-3ln + 2lnx = 15ln + -1lnx

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-3ln + -15ln + 2lnx = 15ln + -15ln + -1lnx

Combine like terms: -3ln + -15ln = -18ln
-18ln + 2lnx = 15ln + -15ln + -1lnx

Combine like terms: 15ln + -15ln = 0
-18ln + 2lnx = 0 + -1lnx
-18ln + 2lnx = -1lnx

Add 'lnx' to each side of the equation.
-18ln + 2lnx + lnx = -1lnx + lnx

Combine like terms: 2lnx + lnx = 3lnx
-18ln + 3lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-18ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-6 + x) = 0

Ignore the factor 3.

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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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