ln(x)+ln(x-2)=ln(63)

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Solution for ln(x)+ln(x-2)=ln(63) equation: 


Simplifying
ln(x) + ln(x + -2) = ln(63)

Multiply ln * x
lnx + ln(x + -2) = ln(63)

Reorder the terms:
lnx + ln(-2 + x) = ln(63)
lnx + (-2 * ln + x * ln) = ln(63)
lnx + (-2ln + lnx) = ln(63)

Reorder the terms:
-2ln + lnx + lnx = ln(63)

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(63)

Reorder the terms for easier multiplication:
-2ln + 2lnx = 63ln

Solving
-2ln + 2lnx = 63ln

Solving for variable 'l'.

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

Add '-63ln' to each side of the equation.
-2ln + -63ln + 2lnx = 63ln + -63ln

Combine like terms: -2ln + -63ln = -65ln
-65ln + 2lnx = 63ln + -63ln

Combine like terms: 63ln + -63ln = 0
-65ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-65 + 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 '(-65 + 2x)' equal to zero and attempt to solve:

Simplifying
-65 + 2x = 0

Solving
-65 + 2x = 0

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

Add '65' to each side of the equation.
-65 + 65 + 2x = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 2x = 0 + 65
2x = 0 + 65

Combine like terms: 0 + 65 = 65
2x = 65

Add '-2x' to each side of the equation.
2x + -2x = 65 + -2x

Combine like terms: 2x + -2x = 0
0 = 65 + -2x

Simplifying
0 = 65 + -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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