ln(x)+ln(x-6)=ln(8)

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Solution for ln(x)+ln(x-6)=ln(8) equation: 


Simplifying
ln(x) + ln(x + -6) = ln(8)

Multiply ln * x
lnx + ln(x + -6) = ln(8)

Reorder the terms:
lnx + ln(-6 + x) = ln(8)
lnx + (-6 * ln + x * ln) = ln(8)
lnx + (-6ln + lnx) = ln(8)

Reorder the terms:
-6ln + lnx + lnx = ln(8)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = ln(8)

Reorder the terms for easier multiplication:
-6ln + 2lnx = 8ln

Solving
-6ln + 2lnx = 8ln

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.
-6ln + -8ln + 2lnx = 8ln + -8ln

Combine like terms: -6ln + -8ln = -14ln
-14ln + 2lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-14ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-7 + x) = 0

Ignore the factor 2.

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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