ln(7x+6)-ln(x)=ln(8)

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Solution for ln(7x+6)-ln(x)=ln(8) equation: 


Simplifying
ln(7x + 6) + -1ln(x) = ln(8)

Reorder the terms:
ln(6 + 7x) + -1ln(x) = ln(8)
(6 * ln + 7x * ln) + -1ln(x) = ln(8)
(6ln + 7lnx) + -1ln(x) = ln(8)

Multiply ln * x
6ln + 7lnx + -1lnx = ln(8)

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

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

Solving
6ln + 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.
6ln + -8ln + 6lnx = 8ln + -8ln

Combine like terms: 6ln + -8ln = -2ln
-2ln + 6lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-2ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-1 + 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 '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Add '-3x' to each side of the equation.
3x + -3x = 1 + -3x

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -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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