ln(7x+15)-ln(x)=ln(8)

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Solution for ln(7x+15)-ln(x)=ln(8) equation: 


Simplifying
ln(7x + 15) + -1ln(x) = ln(8)

Reorder the terms:
ln(15 + 7x) + -1ln(x) = ln(8)
(15 * ln + 7x * ln) + -1ln(x) = ln(8)
(15ln + 7lnx) + -1ln(x) = ln(8)

Multiply ln * x
15ln + 7lnx + -1lnx = ln(8)

Combine like terms: 7lnx + -1lnx = 6lnx
15ln + 6lnx = ln(8)

Reorder the terms for easier multiplication:
15ln + 6lnx = 8ln

Solving
15ln + 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.
15ln + -8ln + 6lnx = 8ln + -8ln

Combine like terms: 15ln + -8ln = 7ln
7ln + 6lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
7ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + 6x) = 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 '(7 + 6x)' equal to zero and attempt to solve:

Simplifying
7 + 6x = 0

Solving
7 + 6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = 0 + -7
6x = 0 + -7

Combine like terms: 0 + -7 = -7
6x = -7

Add '-6x' to each side of the equation.
6x + -6x = -7 + -6x

Combine like terms: 6x + -6x = 0
0 = -7 + -6x

Simplifying
0 = -7 + -6x

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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