ln(x)+ln(x+1)+ln(2)=ln(24)

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Solution for ln(x)+ln(x+1)+ln(2)=ln(24) equation:


Simplifying
ln(x) + ln(x + 1) + ln(2) = ln(24)

Multiply ln * x
lnx + ln(x + 1) + ln(2) = ln(24)

Reorder the terms:
lnx + ln(1 + x) + ln(2) = ln(24)
lnx + (1 * ln + x * ln) + ln(2) = ln(24)
lnx + (1ln + lnx) + ln(2) = ln(24)

Reorder the terms for easier multiplication:
lnx + 1ln + lnx + 2ln = ln(24)

Reorder the terms:
1ln + 2ln + lnx + lnx = ln(24)

Combine like terms: 1ln + 2ln = 3ln
3ln + lnx + lnx = ln(24)

Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = ln(24)

Reorder the terms for easier multiplication:
3ln + 2lnx = 24ln

Solving
3ln + 2lnx = 24ln

Solving for variable 'l'.

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

Add '-24ln' to each side of the equation.
3ln + -24ln + 2lnx = 24ln + -24ln

Combine like terms: 3ln + -24ln = -21ln
-21ln + 2lnx = 24ln + -24ln

Combine like terms: 24ln + -24ln = 0
-21ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 2x) = 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 '(-21 + 2x)' equal to zero and attempt to solve: Simplifying -21 + 2x = 0 Solving -21 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x = 0 + 21 2x = 0 + 21 Combine like terms: 0 + 21 = 21 2x = 21 Add '-2x' to each side of the equation. 2x + -2x = 21 + -2x Combine like terms: 2x + -2x = 0 0 = 21 + -2x Simplifying 0 = 21 + -2x 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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