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

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


Simplifying
0 = In(x + 1) + In(2x)

Reorder the terms:
0 = nI(1 + x) + In(2x)
0 = (1 * nI + x * nI) + In(2x)
0 = (1nI + nxI) + In(2x)

Remove parenthesis around (2x)
0 = 1nI + nxI + nI * 2x

Reorder the terms for easier multiplication:
0 = 1nI + nxI + 2nI * x

Multiply nI * x
0 = 1nI + nxI + 2nxI

Combine like terms: nxI + 2nxI = 3nxI
0 = 1nI + 3nxI

Solving
0 = 1nI + 3nxI

Solving for variable 'n'.

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

Add '-1nI' to each side of the equation.
0 + -1nI = 1nI + -1nI + 3nxI
Remove the zero:
-1nI = 1nI + -1nI + 3nxI

Combine like terms: 1nI + -1nI = 0
-1nI = 0 + 3nxI
-1nI = 3nxI

Add '-3nxI' to each side of the equation.
-1nI + -3nxI = 3nxI + -3nxI

Combine like terms: 3nxI + -3nxI = 0
-1nI + -3nxI = 0

Factor out the Greatest Common Factor (GCF), '-1nI'.
-1nI(1 + 3x) = 0

Ignore the factor -1.

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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -3x 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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