ln(x)+ln(x-2)=ln(48)

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Solution for ln(x)+ln(x-2)=ln(48) equation: 


Simplifying
ln(x) + ln(x + -2) = ln(48)

Multiply ln * x
lnx + ln(x + -2) = ln(48)

Reorder the terms:
lnx + ln(-2 + x) = ln(48)
lnx + (-2 * ln + x * ln) = ln(48)
lnx + (-2ln + lnx) = ln(48)

Reorder the terms:
-2ln + lnx + lnx = ln(48)

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(48)

Reorder the terms for easier multiplication:
-2ln + 2lnx = 48ln

Solving
-2ln + 2lnx = 48ln

Solving for variable 'l'.

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

Add '-48ln' to each side of the equation.
-2ln + -48ln + 2lnx = 48ln + -48ln

Combine like terms: -2ln + -48ln = -50ln
-50ln + 2lnx = 48ln + -48ln

Combine like terms: 48ln + -48ln = 0
-50ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-25 + 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 '(-25 + x)' equal to zero and attempt to solve:

Simplifying
-25 + x = 0

Solving
-25 + x = 0

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

Add '25' to each side of the equation.
-25 + 25 + x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x = 0 + 25
x = 0 + 25

Combine like terms: 0 + 25 = 25
x = 25

Add '-1x' to each side of the equation.
x + -1x = 25 + -1x

Combine like terms: x + -1x = 0
0 = 25 + -1x

Simplifying
0 = 25 + -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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