ln(x)+ln(x-5)=ln(24)

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Solution for ln(x)+ln(x-5)=ln(24) equation: 


Simplifying
ln(x) + ln(x + -5) = ln(24)

Multiply ln * x
lnx + ln(x + -5) = ln(24)

Reorder the terms:
lnx + ln(-5 + x) = ln(24)
lnx + (-5 * ln + x * ln) = ln(24)
lnx + (-5ln + lnx) = ln(24)

Reorder the terms:
-5ln + lnx + lnx = ln(24)

Combine like terms: lnx + lnx = 2lnx
-5ln + 2lnx = ln(24)

Reorder the terms for easier multiplication:
-5ln + 2lnx = 24ln

Solving
-5ln + 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.
-5ln + -24ln + 2lnx = 24ln + -24ln

Combine like terms: -5ln + -24ln = -29ln
-29ln + 2lnx = 24ln + -24ln

Combine like terms: 24ln + -24ln = 0
-29ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-29 + 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 '(-29 + 2x)' equal to zero and attempt to solve:

Simplifying
-29 + 2x = 0

Solving
-29 + 2x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 2x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 2x = 0 + 29
2x = 0 + 29

Combine like terms: 0 + 29 = 29
2x = 29

Add '-2x' to each side of the equation.
2x + -2x = 29 + -2x

Combine like terms: 2x + -2x = 0
0 = 29 + -2x

Simplifying
0 = 29 + -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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