ln(x+3)+ln(x)=ln(x+24)

Solution for ln(x+3)+ln(x)=ln(x+24) equation:

Simplifying
ln(x + 3) + ln(x) = ln(x + 24)

Reorder the terms:
ln(3 + x) + ln(x) = ln(x + 24)
(3 * ln + x * ln) + ln(x) = ln(x + 24)
(3ln + lnx) + ln(x) = ln(x + 24)

Multiply ln * x
3ln + lnx + lnx = ln(x + 24)

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

Reorder the terms:
3ln + 2lnx = ln(24 + x)
3ln + 2lnx = (24 * ln + x * ln)
3ln + 2lnx = (24ln + lnx)

Solving
3ln + 2lnx = 24ln + lnx

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 + lnx

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

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

Add '-1lnx' to each side of the equation.
-21ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-21ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-21ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-21 + x = 0

Solving
-21 + x = 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 + x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + x = 0 + 21
x = 0 + 21

Combine like terms: 0 + 21 = 21
x = 21

Add '-1x' to each side of the equation.
x + -1x = 21 + -1x

Combine like terms: x + -1x = 0
0 = 21 + -1x

Simplifying
0 = 21 + -1x

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.