ln(x+15)-lnx=ln(x-1)

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Solution for ln(x+15)-lnx=ln(x-1) equation:


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

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

Combine like terms: lnx + -1lnx = 0
15ln + 0 = ln(x + -1)
15ln = ln(x + -1)

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

Solving
15ln = -1ln + lnx

Solving for variable 'l'.

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

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

Combine like terms: 15ln + ln = 16ln
16ln = -1ln + ln + lnx

Combine like terms: -1ln + ln = 0
16ln = 0 + lnx
16ln = lnx

Add '-1lnx' to each side of the equation.
16ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
16ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(16 + -1x) = 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 '(16 + -1x)' equal to zero and attempt to solve: Simplifying 16 + -1x = 0 Solving 16 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1x = 0 + -16 -1x = 0 + -16 Combine like terms: 0 + -16 = -16 -1x = -16 Add 'x' to each side of the equation. -1x + x = -16 + x Combine like terms: -1x + x = 0 0 = -16 + x Simplifying 0 = -16 + x 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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