ln(x)+ln(x-1)=ln(x-8)

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Solution for ln(x)+ln(x-1)=ln(x-8) equation: 


Simplifying
ln(x) + ln(x + -1) = ln(x + -8)

Multiply ln * x
lnx + ln(x + -1) = ln(x + -8)

Reorder the terms:
lnx + ln(-1 + x) = ln(x + -8)
lnx + (-1 * ln + x * ln) = ln(x + -8)
lnx + (-1ln + lnx) = ln(x + -8)

Reorder the terms:
-1ln + lnx + lnx = ln(x + -8)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(x + -8)

Reorder the terms:
-1ln + 2lnx = ln(-8 + x)
-1ln + 2lnx = (-8 * ln + x * ln)
-1ln + 2lnx = (-8ln + lnx)

Solving
-1ln + 2lnx = -8ln + lnx

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
-1ln + 8ln + 2lnx = -8ln + 8ln + lnx

Combine like terms: -1ln + 8ln = 7ln
7ln + 2lnx = -8ln + 8ln + lnx

Combine like terms: -8ln + 8ln = 0
7ln + 2lnx = 0 + lnx
7ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
7ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
7ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
7ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + 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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Add '-1x' to each side of the equation.
x + -1x = -7 + -1x

Combine like terms: x + -1x = 0
0 = -7 + -1x

Simplifying
0 = -7 + -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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