3In(x)=In(16)+In(4)

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Solution for 3In(x)=In(16)+In(4) equation:


Simplifying
3In(x) = In(16) + In(4)

Multiply nI * x
3nxI = In(16) + In(4)

Reorder the terms for easier multiplication:
3nxI = 16nI + In(4)

Reorder the terms for easier multiplication:
3nxI = 16nI + 4nI

Combine like terms: 16nI + 4nI = 20nI
3nxI = 20nI

Solving
3nxI = 20nI

Solving for variable 'n'.

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

Add '-20nI' to each side of the equation.
-20nI + 3nxI = 20nI + -20nI

Combine like terms: 20nI + -20nI = 0
-20nI + 3nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(-20 + 3x) = 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 '(-20 + 3x)' equal to zero and attempt to solve: Simplifying -20 + 3x = 0 Solving -20 + 3x = 0 Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + 3x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3x = 0 + 20 3x = 0 + 20 Combine like terms: 0 + 20 = 20 3x = 20 Add '-3x' to each side of the equation. 3x + -3x = 20 + -3x Combine like terms: 3x + -3x = 0 0 = 20 + -3x Simplifying 0 = 20 + -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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