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

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

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

Reorder the terms:
nL(8 + 7x) + -1ln(x) = ln(8)
(8 * nL + 7x * nL) + -1ln(x) = ln(8)
(8nL + 7nxL) + -1ln(x) = ln(8)

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

Reorder the terms:
-1lnx + 8nL + 7nxL = ln(8)

Reorder the terms for easier multiplication:
-1lnx + 8nL + 7nxL = 8ln

Solving
-1lnx + 8nL + 7nxL = 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.
-1lnx + 8nL + -8ln + 7nxL = 8ln + -8ln

Reorder the terms:
-8ln + -1lnx + 8nL + 7nxL = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-8ln + -1lnx + 8nL + 7nxL = 0

Add '-8nL' to each side of the equation.
-8ln + -1lnx + 8nL + -8nL + 7nxL = 0 + -8nL

Combine like terms: 8nL + -8nL = 0
-8ln + -1lnx + 0 + 7nxL = 0 + -8nL
-8ln + -1lnx + 7nxL = 0 + -8nL
Remove the zero:
-8ln + -1lnx + 7nxL = -8nL

Add '-7nxL' to each side of the equation.
-8ln + -1lnx + 7nxL + -7nxL = -8nL + -7nxL

Combine like terms: 7nxL + -7nxL = 0
-8ln + -1lnx + 0 = -8nL + -7nxL
-8ln + -1lnx = -8nL + -7nxL

Reorder the terms:
-8ln + -1lnx + 8nL + 7nxL = -8nL + 8nL + -7nxL + 7nxL

Combine like terms: -8nL + 8nL = 0
-8ln + -1lnx + 8nL + 7nxL = 0 + -7nxL + 7nxL
-8ln + -1lnx + 8nL + 7nxL = -7nxL + 7nxL

Combine like terms: -7nxL + 7nxL = 0
-8ln + -1lnx + 8nL + 7nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-8l + -1lx + 8L + 7xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-8l + -1lx + 8L + 7xL)' equal to zero and attempt to solve:

Simplifying
-8l + -1lx + 8L + 7xL = 0

Reorder the terms:
8L + -8l + -1lx + 7xL = 0

Solving
8L + -8l + -1lx + 7xL = 0

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

Add '-8L' to each side of the equation.
8L + -8l + -1lx + -8L + 7xL = 0 + -8L

Reorder the terms:
8L + -8L + -8l + -1lx + 7xL = 0 + -8L

Combine like terms: 8L + -8L = 0
0 + -8l + -1lx + 7xL = 0 + -8L
-8l + -1lx + 7xL = 0 + -8L
Remove the zero:
-8l + -1lx + 7xL = -8L

Add '-7xL' to each side of the equation.
-8l + -1lx + 7xL + -7xL = -8L + -7xL

Combine like terms: 7xL + -7xL = 0
-8l + -1lx + 0 = -8L + -7xL
-8l + -1lx = -8L + -7xL

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.