In(3x+7)+In(x-2)=Ine

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Solution for In(3x+7)+In(x-2)=Ine equation:


Simplifying
In(3x + 7) + In(x + -2) = Ine

Reorder the terms:
nI(7 + 3x) + In(x + -2) = Ine
(7 * nI + 3x * nI) + In(x + -2) = Ine
(7nI + 3nxI) + In(x + -2) = Ine

Reorder the terms:
7nI + 3nxI + nI(-2 + x) = Ine
7nI + 3nxI + (-2 * nI + x * nI) = Ine
7nI + 3nxI + (-2nI + nxI) = Ine

Reorder the terms:
7nI + -2nI + 3nxI + nxI = Ine

Combine like terms: 7nI + -2nI = 5nI
5nI + 3nxI + nxI = Ine

Combine like terms: 3nxI + nxI = 4nxI
5nI + 4nxI = Ine

Solving
5nI + 4nxI = enI

Solving for variable 'n'.

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

Add '-1enI' to each side of the equation.
5nI + -1enI + 4nxI = enI + -1enI

Reorder the terms:
-1enI + 5nI + 4nxI = enI + -1enI

Combine like terms: enI + -1enI = 0
-1enI + 5nI + 4nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(-1e + 5 + 4x) = 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 '(-1e + 5 + 4x)' equal to zero and attempt to solve: Simplifying -1e + 5 + 4x = 0 Reorder the terms: 5 + -1e + 4x = 0 Solving 5 + -1e + 4x = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -1e + -5 + 4x = 0 + -5 Reorder the terms: 5 + -5 + -1e + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1e + 4x = 0 + -5 -1e + 4x = 0 + -5 Combine like terms: 0 + -5 = -5 -1e + 4x = -5 Add 'e' to each side of the equation. -1e + e + 4x = -5 + e Combine like terms: -1e + e = 0 0 + 4x = -5 + e 4x = -5 + e Add '-4x' to each side of the equation. 4x + -4x = -5 + e + -4x Combine like terms: 4x + -4x = 0 0 = -5 + e + -4x Simplifying 0 = -5 + e + -4x 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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