ln(7x+4)-ln(x)=ln(8)

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Solution for ln(7x+4)-ln(x)=ln(8) equation: 


Simplifying
ln(7x + 4) + -1ln(x) = ln(8)

Reorder the terms:
ln(4 + 7x) + -1ln(x) = ln(8)
(4 * ln + 7x * ln) + -1ln(x) = ln(8)
(4ln + 7lnx) + -1ln(x) = ln(8)

Multiply ln * x
4ln + 7lnx + -1lnx = ln(8)

Combine like terms: 7lnx + -1lnx = 6lnx
4ln + 6lnx = ln(8)

Reorder the terms for easier multiplication:
4ln + 6lnx = 8ln

Solving
4ln + 6lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
4ln + -8ln + 6lnx = 8ln + -8ln

Combine like terms: 4ln + -8ln = -4ln
-4ln + 6lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-4ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-2 + 3x) = 0

Ignore the factor 2.

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 '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Add '-3x' to each side of the equation.
3x + -3x = 2 + -3x

Combine like terms: 3x + -3x = 0
0 = 2 + -3x

Simplifying
0 = 2 + -3x

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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