In(x+4)-In(8)=In(5)

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Solution for In(x+4)-In(8)=In(5) equation:


Simplifying
In(x + 4) + -1In(8) = In(5)

Reorder the terms:
nI(4 + x) + -1In(8) = In(5)
(4 * nI + x * nI) + -1In(8) = In(5)
(4nI + nxI) + -1In(8) = In(5)

Reorder the terms for easier multiplication:
4nI + nxI + -1 * 8nI = In(5)

Multiply -1 * 8
4nI + nxI + -8nI = In(5)

Reorder the terms:
4nI + -8nI + nxI = In(5)

Combine like terms: 4nI + -8nI = -4nI
-4nI + nxI = In(5)

Reorder the terms for easier multiplication:
-4nI + nxI = 5nI

Solving
-4nI + nxI = 5nI

Solving for variable 'n'.

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

Add '-5nI' to each side of the equation.
-4nI + -5nI + nxI = 5nI + -5nI

Combine like terms: -4nI + -5nI = -9nI
-9nI + nxI = 5nI + -5nI

Combine like terms: 5nI + -5nI = 0
-9nI + nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(-9 + x) = 0

Subproblem 1

Set the factor 'nI' equal to zero and attempt to solve: Simplifying nI = 0 Solving nI = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nI = 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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