ln(x-7)-ln(8)=ln(19)

Solution for ln(x-7)-ln(8)=ln(19) equation:

Simplifying
ln(x + -7) + -1ln(8) = ln(19)

Reorder the terms:
ln(-7 + x) + -1ln(8) = ln(19)
(-7 * ln + x * ln) + -1ln(8) = ln(19)
(-7ln + lnx) + -1ln(8) = ln(19)

Reorder the terms for easier multiplication:
-7ln + lnx + -1 * 8ln = ln(19)

Multiply -1 * 8
-7ln + lnx + -8ln = ln(19)

Reorder the terms:
-7ln + -8ln + lnx = ln(19)

Combine like terms: -7ln + -8ln = -15ln
-15ln + lnx = ln(19)

Reorder the terms for easier multiplication:
-15ln + lnx = 19ln

Solving
-15ln + 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.
-15ln + -19ln + lnx = 19ln + -19ln

Combine like terms: -15ln + -19ln = -34ln
-34ln + lnx = 19ln + -19ln

Combine like terms: 19ln + -19ln = 0
-34ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-34 + 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 '(-34 + x)' equal to zero and attempt to solve:

Simplifying
-34 + x = 0

Solving
-34 + x = 0

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

Add '34' to each side of the equation.
-34 + 34 + x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + x = 0 + 34
x = 0 + 34

Combine like terms: 0 + 34 = 34
x = 34

Add '-1x' to each side of the equation.
x + -1x = 34 + -1x

Combine like terms: x + -1x = 0
0 = 34 + -1x

Simplifying
0 = 34 + -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.