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

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

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

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

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

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

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

Solving
5ln + 2lnx = 4ln

Solving for variable 'l'.

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

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

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

Combine like terms: 4ln + -4ln = 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.