ln(x)+ln(x-9)=ln(22)

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Solution for ln(x)+ln(x-9)=ln(22) equation: 


Simplifying
ln(x) + ln(x + -9) = ln(22)

Multiply ln * x
lnx + ln(x + -9) = ln(22)

Reorder the terms:
lnx + ln(-9 + x) = ln(22)
lnx + (-9 * ln + x * ln) = ln(22)
lnx + (-9ln + lnx) = ln(22)

Reorder the terms:
-9ln + lnx + lnx = ln(22)

Combine like terms: lnx + lnx = 2lnx
-9ln + 2lnx = ln(22)

Reorder the terms for easier multiplication:
-9ln + 2lnx = 22ln

Solving
-9ln + 2lnx = 22ln

Solving for variable 'l'.

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

Add '-22ln' to each side of the equation.
-9ln + -22ln + 2lnx = 22ln + -22ln

Combine like terms: -9ln + -22ln = -31ln
-31ln + 2lnx = 22ln + -22ln

Combine like terms: 22ln + -22ln = 0
-31ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-31 + 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 '(-31 + 2x)' equal to zero and attempt to solve:

Simplifying
-31 + 2x = 0

Solving
-31 + 2x = 0

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

Add '31' to each side of the equation.
-31 + 31 + 2x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2x = 0 + 31
2x = 0 + 31

Combine like terms: 0 + 31 = 31
2x = 31

Add '-2x' to each side of the equation.
2x + -2x = 31 + -2x

Combine like terms: 2x + -2x = 0
0 = 31 + -2x

Simplifying
0 = 31 + -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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