ln(x)+ln(x-4)=ln(45)

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Solution for ln(x)+ln(x-4)=ln(45) equation: 


Simplifying
ln(x) + ln(x + -4) = ln(45)

Multiply ln * x
lnx + ln(x + -4) = ln(45)

Reorder the terms:
lnx + ln(-4 + x) = ln(45)
lnx + (-4 * ln + x * ln) = ln(45)
lnx + (-4ln + lnx) = ln(45)

Reorder the terms:
-4ln + lnx + lnx = ln(45)

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx = ln(45)

Reorder the terms for easier multiplication:
-4ln + 2lnx = 45ln

Solving
-4ln + 2lnx = 45ln

Solving for variable 'l'.

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

Add '-45ln' to each side of the equation.
-4ln + -45ln + 2lnx = 45ln + -45ln

Combine like terms: -4ln + -45ln = -49ln
-49ln + 2lnx = 45ln + -45ln

Combine like terms: 45ln + -45ln = 0
-49ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-49 + 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 '(-49 + 2x)' equal to zero and attempt to solve:

Simplifying
-49 + 2x = 0

Solving
-49 + 2x = 0

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

Add '49' to each side of the equation.
-49 + 49 + 2x = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 2x = 0 + 49
2x = 0 + 49

Combine like terms: 0 + 49 = 49
2x = 49

Add '-2x' to each side of the equation.
2x + -2x = 49 + -2x

Combine like terms: 2x + -2x = 0
0 = 49 + -2x

Simplifying
0 = 49 + -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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