ln(x+5)-ln(5)=ln(20)

Solution for ln(x+5)-ln(5)=ln(20) equation:

Simplifying
ln(x + 5) + -1ln(5) = ln(20)

Reorder the terms:
ln(5 + x) + -1ln(5) = ln(20)
(5 * ln + x * ln) + -1ln(5) = ln(20)
(5ln + lnx) + -1ln(5) = ln(20)

Reorder the terms for easier multiplication:
5ln + lnx + -1 * 5ln = ln(20)

Multiply -1 * 5
5ln + lnx + -5ln = ln(20)

Reorder the terms:
5ln + -5ln + lnx = ln(20)

Combine like terms: 5ln + -5ln = 0
0 + lnx = ln(20)
lnx = ln(20)

Reorder the terms for easier multiplication:
lnx = 20ln

Solving
lnx = 20ln

Solving for variable 'l'.

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

Add '-20ln' to each side of the equation.
-20ln + lnx = 20ln + -20ln

Combine like terms: 20ln + -20ln = 0
-20ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-20 + x) = 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 '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Add '-1x' to each side of the equation.
x + -1x = 20 + -1x

Combine like terms: x + -1x = 0
0 = 20 + -1x

Simplifying
0 = 20 + -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.