ln(x)+ln(x+4)=ln(5)

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Solution for ln(x)+ln(x+4)=ln(5) equation: 


Simplifying
ln(x) + ln(x + 4) = ln(5)

Multiply ln * x
lnx + ln(x + 4) = ln(5)

Reorder the terms:
lnx + ln(4 + x) = ln(5)
lnx + (4 * ln + x * ln) = ln(5)
lnx + (4ln + lnx) = ln(5)

Reorder the terms:
4ln + lnx + lnx = ln(5)

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(5)

Reorder the terms for easier multiplication:
4ln + 2lnx = 5ln

Solving
4ln + 2lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
4ln + -5ln + 2lnx = 5ln + -5ln

Combine like terms: 4ln + -5ln = -1ln
-1ln + 2lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-1ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

Combine like terms: 2x + -2x = 0
0 = 1 + -2x

Simplifying
0 = 1 + -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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