ln(x-5)+ln(4)=ln(19)

Solution for ln(x-5)+ln(4)=ln(19) equation:

Simplifying
ln(x + -5) + ln(4) = ln(19)

Reorder the terms:
ln(-5 + x) + ln(4) = ln(19)
(-5 * ln + x * ln) + ln(4) = ln(19)
(-5ln + lnx) + ln(4) = ln(19)

Reorder the terms for easier multiplication:
-5ln + lnx + 4ln = ln(19)

Reorder the terms:
-5ln + 4ln + lnx = ln(19)

Combine like terms: -5ln + 4ln = -1ln
-1ln + lnx = ln(19)

Reorder the terms for easier multiplication:
-1ln + lnx = 19ln

Solving
-1ln + lnx = 19ln

Solving for variable 'l'.

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

Add '-19ln' to each side of the equation.
-1ln + -19ln + lnx = 19ln + -19ln

Combine like terms: -1ln + -19ln = -20ln
-20ln + lnx = 19ln + -19ln

Combine like terms: 19ln + -19ln = 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.