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

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


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

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

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