ln(7)=ln(x-7)-ln(4)

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Solution for ln(7)=ln(x-7)-ln(4) equation: 


Simplifying
ln(7) = ln(x + -7) + -1ln(4)

Reorder the terms for easier multiplication:
7ln = ln(x + -7) + -1ln(4)

Reorder the terms:
7ln = ln(-7 + x) + -1ln(4)
7ln = (-7 * ln + x * ln) + -1ln(4)
7ln = (-7ln + lnx) + -1ln(4)

Reorder the terms for easier multiplication:
7ln = -7ln + lnx + -1 * 4ln

Multiply -1 * 4
7ln = -7ln + lnx + -4ln

Reorder the terms:
7ln = -7ln + -4ln + lnx

Combine like terms: -7ln + -4ln = -11ln
7ln = -11ln + lnx

Solving
7ln = -11ln + lnx

Solving for variable 'l'.

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

Add '11ln' to each side of the equation.
7ln + 11ln = -11ln + 11ln + lnx

Combine like terms: 7ln + 11ln = 18ln
18ln = -11ln + 11ln + lnx

Combine like terms: -11ln + 11ln = 0
18ln = 0 + lnx
18ln = lnx

Add '-1lnx' to each side of the equation.
18ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
18ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(18 + -1x) = 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 '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Add 'x' to each side of the equation.
-1x + x = -18 + x

Combine like terms: -1x + x = 0
0 = -18 + x

Simplifying
0 = -18 + x

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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