ln(x)+ln(x-4)=ln(165)

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Solution for ln(x)+ln(x-4)=ln(165) equation: 


Simplifying
ln(x) + ln(x + -4) = ln(165)

Multiply ln * x
lnx + ln(x + -4) = ln(165)

Reorder the terms:
lnx + ln(-4 + x) = ln(165)
lnx + (-4 * ln + x * ln) = ln(165)
lnx + (-4ln + lnx) = ln(165)

Reorder the terms:
-4ln + lnx + lnx = ln(165)

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx = ln(165)

Reorder the terms for easier multiplication:
-4ln + 2lnx = 165ln

Solving
-4ln + 2lnx = 165ln

Solving for variable 'l'.

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

Add '-165ln' to each side of the equation.
-4ln + -165ln + 2lnx = 165ln + -165ln

Combine like terms: -4ln + -165ln = -169ln
-169ln + 2lnx = 165ln + -165ln

Combine like terms: 165ln + -165ln = 0
-169ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-169 + 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 '(-169 + 2x)' equal to zero and attempt to solve:

Simplifying
-169 + 2x = 0

Solving
-169 + 2x = 0

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

Add '169' to each side of the equation.
-169 + 169 + 2x = 0 + 169

Combine like terms: -169 + 169 = 0
0 + 2x = 0 + 169
2x = 0 + 169

Combine like terms: 0 + 169 = 169
2x = 169

Add '-2x' to each side of the equation.
2x + -2x = 169 + -2x

Combine like terms: 2x + -2x = 0
0 = 169 + -2x

Simplifying
0 = 169 + -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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