ln(6x+5)-ln(x)=ln(7)

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Solution for ln(6x+5)-ln(x)=ln(7) equation: 


Simplifying
ln(6x + 5) + -1ln(x) = ln(7)

Reorder the terms:
ln(5 + 6x) + -1ln(x) = ln(7)
(5 * ln + 6x * ln) + -1ln(x) = ln(7)
(5ln + 6lnx) + -1ln(x) = ln(7)

Multiply ln * x
5ln + 6lnx + -1lnx = ln(7)

Combine like terms: 6lnx + -1lnx = 5lnx
5ln + 5lnx = ln(7)

Reorder the terms for easier multiplication:
5ln + 5lnx = 7ln

Solving
5ln + 5lnx = 7ln

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
5ln + -7ln + 5lnx = 7ln + -7ln

Combine like terms: 5ln + -7ln = -2ln
-2ln + 5lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-2ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 5x) = 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 '(-2 + 5x)' equal to zero and attempt to solve:

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 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 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Add '-5x' to each side of the equation.
5x + -5x = 2 + -5x

Combine like terms: 5x + -5x = 0
0 = 2 + -5x

Simplifying
0 = 2 + -5x

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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