ln(x)+ln(x+1)=3ln(x)

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Solution for ln(x)+ln(x+1)=3ln(x) equation:


Simplifying
ln(x) + ln(x + 1) = 3ln(x)

Multiply ln * x
lnx + ln(x + 1) = 3ln(x)

Reorder the terms:
lnx + ln(1 + x) = 3ln(x)
lnx + (1 * ln + x * ln) = 3ln(x)
lnx + (1ln + lnx) = 3ln(x)

Reorder the terms:
1ln + lnx + lnx = 3ln(x)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = 3ln(x)

Multiply ln * x
1ln + 2lnx = 3lnx

Solving
1ln + 2lnx = 3lnx

Solving for variable 'l'.

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

Add '-3lnx' to each side of the equation.
1ln + 2lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 2lnx + -3lnx = -1lnx
1ln + -1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
1ln + -1lnx = 0

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

Subproblem 1

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