lnx+ln(x-7)=ln(4x-24)

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Solution for lnx+ln(x-7)=ln(4x-24) equation: 


Simplifying
lnx + ln(x + -7) = ln(4x + -24)

Reorder the terms:
lnx + ln(-7 + x) = ln(4x + -24)
lnx + (-7 * ln + x * ln) = ln(4x + -24)
lnx + (-7ln + lnx) = ln(4x + -24)

Reorder the terms:
-7ln + lnx + lnx = ln(4x + -24)

Combine like terms: lnx + lnx = 2lnx
-7ln + 2lnx = ln(4x + -24)

Reorder the terms:
-7ln + 2lnx = ln(-24 + 4x)
-7ln + 2lnx = (-24 * ln + 4x * ln)
-7ln + 2lnx = (-24ln + 4lnx)

Solving
-7ln + 2lnx = -24ln + 4lnx

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.
-7ln + 24ln + 2lnx = -24ln + 24ln + 4lnx

Combine like terms: -7ln + 24ln = 17ln
17ln + 2lnx = -24ln + 24ln + 4lnx

Combine like terms: -24ln + 24ln = 0
17ln + 2lnx = 0 + 4lnx
17ln + 2lnx = 4lnx

Add '-4lnx' to each side of the equation.
17ln + 2lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 2lnx + -4lnx = -2lnx
17ln + -2lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
17ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(17 + -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 '(17 + -2x)' equal to zero and attempt to solve:

Simplifying
17 + -2x = 0

Solving
17 + -2x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2x = 0 + -17
-2x = 0 + -17

Combine like terms: 0 + -17 = -17
-2x = -17

Add '2x' to each side of the equation.
-2x + 2x = -17 + 2x

Combine like terms: -2x + 2x = 0
0 = -17 + 2x

Simplifying
0 = -17 + 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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