Lny=ln(5y-8)

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Solution for Lny=ln(5y-8) equation: 


Simplifying
Lny = ln(5y + -8)

Reorder the terms:
nyL = ln(-8 + 5y)
nyL = (-8 * ln + 5y * ln)
nyL = (-8ln + 5lny)

Solving
nyL = -8ln + 5lny

Solving for variable 'n'.

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

Add '8ln' to each side of the equation.
8ln + nyL = -8ln + 8ln + 5lny

Combine like terms: -8ln + 8ln = 0
8ln + nyL = 0 + 5lny
8ln + nyL = 5lny

Add '-5lny' to each side of the equation.
8ln + -5lny + nyL = 5lny + -5lny

Combine like terms: 5lny + -5lny = 0
8ln + -5lny + nyL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8l + -5ly + yL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(8l + -5ly + yL)' equal to zero and attempt to solve:

Simplifying
8l + -5ly + yL = 0

Solving
8l + -5ly + yL = 0

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

Add '-8l' to each side of the equation.
8l + -5ly + -8l + yL = 0 + -8l

Reorder the terms:
8l + -8l + -5ly + yL = 0 + -8l

Combine like terms: 8l + -8l = 0
0 + -5ly + yL = 0 + -8l
-5ly + yL = 0 + -8l
Remove the zero:
-5ly + yL = -8l

Add '5ly' to each side of the equation.
-5ly + 5ly + yL = -8l + 5ly

Combine like terms: -5ly + 5ly = 0
0 + yL = -8l + 5ly
yL = -8l + 5ly

Add '-1yL' to each side of the equation.
yL + -1yL = -8l + 5ly + -1yL

Combine like terms: yL + -1yL = 0
0 = -8l + 5ly + -1yL

Simplifying
0 = -8l + 5ly + -1yL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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