ln(3)+ln(6-x)-ln(x)=0

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Solution for ln(3)+ln(6-x)-ln(x)=0 equation: 


Simplifying
ln(3) + ln(6 + -1x) + -1ln(x) = 0

Reorder the terms for easier multiplication:
3ln + ln(6 + -1x) + -1ln(x) = 0
3ln + (6 * ln + -1x * ln) + -1ln(x) = 0
3ln + (6ln + -1lnx) + -1ln(x) = 0

Multiply ln * x
3ln + 6ln + -1lnx + -1lnx = 0

Combine like terms: 3ln + 6ln = 9ln
9ln + -1lnx + -1lnx = 0

Combine like terms: -1lnx + -1lnx = -2lnx
9ln + -2lnx = 0

Solving
9ln + -2lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(9 + -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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Add '2x' to each side of the equation.
-2x + 2x = -9 + 2x

Combine like terms: -2x + 2x = 0
0 = -9 + 2x

Simplifying
0 = -9 + 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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