ln(x)+ln(x+3)=In(20-5x)

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Solution for ln(x)+ln(x+3)=In(20-5x) equation:


Simplifying
ln(x) + ln(x + 3) = In(20 + -5x)

Multiply ln * x
lnx + ln(x + 3) = In(20 + -5x)

Reorder the terms:
lnx + ln(3 + x) = In(20 + -5x)
lnx + (3 * ln + x * ln) = In(20 + -5x)
lnx + (3ln + lnx) = In(20 + -5x)

Reorder the terms:
3ln + lnx + lnx = In(20 + -5x)

Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = In(20 + -5x)
3ln + 2lnx = (20 * nI + -5x * nI)
3ln + 2lnx = (20nI + -5nxI)

Solving
3ln + 2lnx = 20nI + -5nxI

Solving for variable 'l'.

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

Reorder the terms:
3ln + 2lnx + -20nI + 5nxI = 20nI + -20nI + -5nxI + 5nxI

Combine like terms: 20nI + -20nI = 0
3ln + 2lnx + -20nI + 5nxI = 0 + -5nxI + 5nxI
3ln + 2lnx + -20nI + 5nxI = -5nxI + 5nxI

Combine like terms: -5nxI + 5nxI = 0
3ln + 2lnx + -20nI + 5nxI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3l + 2lx + -20I + 5xI) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(3l + 2lx + -20I + 5xI)' equal to zero and attempt to solve: Simplifying 3l + 2lx + -20I + 5xI = 0 Reorder the terms: -20I + 3l + 2lx + 5xI = 0 Solving -20I + 3l + 2lx + 5xI = 0 Move all terms containing l to the left, all other terms to the right. Add '20I' to each side of the equation. -20I + 3l + 2lx + 20I + 5xI = 0 + 20I Reorder the terms: -20I + 20I + 3l + 2lx + 5xI = 0 + 20I Combine like terms: -20I + 20I = 0 0 + 3l + 2lx + 5xI = 0 + 20I 3l + 2lx + 5xI = 0 + 20I Remove the zero: 3l + 2lx + 5xI = 20I Add '-5xI' to each side of the equation. 3l + 2lx + 5xI + -5xI = 20I + -5xI Combine like terms: 5xI + -5xI = 0 3l + 2lx + 0 = 20I + -5xI 3l + 2lx = 20I + -5xI 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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