In(3x+4)=2In(x+1)

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Solution for In(3x+4)=2In(x+1) equation:


Simplifying
In(3x + 4) = 2In(x + 1)

Reorder the terms:
nI(4 + 3x) = 2In(x + 1)
(4 * nI + 3x * nI) = 2In(x + 1)
(4nI + 3nxI) = 2In(x + 1)

Reorder the terms:
4nI + 3nxI = 2nI(1 + x)
4nI + 3nxI = (1 * 2nI + x * 2nI)
4nI + 3nxI = (2nI + 2nxI)

Solving
4nI + 3nxI = 2nI + 2nxI

Solving for variable 'n'.

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

Add '-2nI' to each side of the equation.
4nI + -2nI + 3nxI = 2nI + -2nI + 2nxI

Combine like terms: 4nI + -2nI = 2nI
2nI + 3nxI = 2nI + -2nI + 2nxI

Combine like terms: 2nI + -2nI = 0
2nI + 3nxI = 0 + 2nxI
2nI + 3nxI = 2nxI

Add '-2nxI' to each side of the equation.
2nI + 3nxI + -2nxI = 2nxI + -2nxI

Combine like terms: 3nxI + -2nxI = 1nxI
2nI + 1nxI = 2nxI + -2nxI

Combine like terms: 2nxI + -2nxI = 0
2nI + 1nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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