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

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


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

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

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

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

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

Combine like terms: lnx + lnx = 2lnx
2lnx = ln(15)

Reorder the terms for easier multiplication:
2lnx = 15ln

Solving
2lnx = 15ln

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.
-15ln + 2lnx = 15ln + -15ln

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Add '-2x' to each side of the equation. 2x + -2x = 15 + -2x Combine like terms: 2x + -2x = 0 0 = 15 + -2x Simplifying 0 = 15 + -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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