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

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.