Ln(-4p+10)=ln(-5p+3)

Solution for Ln(-4p+10)=ln(-5p+3) equation:

Simplifying
Ln(-4p + 10) = ln(-5p + 3)

Reorder the terms:
nL(10 + -4p) = ln(-5p + 3)
(10 * nL + -4p * nL) = ln(-5p + 3)
(10nL + -4npL) = ln(-5p + 3)

Reorder the terms:
10nL + -4npL = ln(3 + -5p)
10nL + -4npL = (3 * ln + -5p * ln)
10nL + -4npL = (3ln + -5lnp)

Solving
10nL + -4npL = 3ln + -5lnp

Solving for variable 'n'.

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

Add '-3ln' to each side of the equation.
10nL + -3ln + -4npL = 3ln + -3ln + -5lnp

Reorder the terms:
-3ln + 10nL + -4npL = 3ln + -3ln + -5lnp

Combine like terms: 3ln + -3ln = 0
-3ln + 10nL + -4npL = 0 + -5lnp
-3ln + 10nL + -4npL = -5lnp

Add '5lnp' to each side of the equation.
-3ln + 10nL + 5lnp + -4npL = -5lnp + 5lnp

Reorder the terms:
-3ln + 5lnp + 10nL + -4npL = -5lnp + 5lnp

Combine like terms: -5lnp + 5lnp = 0
-3ln + 5lnp + 10nL + -4npL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + 5lp + 10L + -4pL) = 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 '(-3l + 5lp + 10L + -4pL)' equal to zero and attempt to solve:

Simplifying
-3l + 5lp + 10L + -4pL = 0

Reorder the terms:
10L + -3l + 5lp + -4pL = 0

Solving
10L + -3l + 5lp + -4pL = 0

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

Add '-10L' to each side of the equation.
10L + -3l + 5lp + -10L + -4pL = 0 + -10L

Reorder the terms:
10L + -10L + -3l + 5lp + -4pL = 0 + -10L

Combine like terms: 10L + -10L = 0
0 + -3l + 5lp + -4pL = 0 + -10L
-3l + 5lp + -4pL = 0 + -10L
Remove the zero:
-3l + 5lp + -4pL = -10L

Add '3l' to each side of the equation.
-3l + 5lp + 3l + -4pL = -10L + 3l

Reorder the terms:
-3l + 3l + 5lp + -4pL = -10L + 3l

Combine like terms: -3l + 3l = 0
0 + 5lp + -4pL = -10L + 3l
5lp + -4pL = -10L + 3l

Add '-5lp' to each side of the equation.
5lp + -5lp + -4pL = -10L + 3l + -5lp

Combine like terms: 5lp + -5lp = 0
0 + -4pL = -10L + 3l + -5lp
-4pL = -10L + 3l + -5lp

Add '4pL' to each side of the equation.
-4pL + 4pL = -10L + 3l + -5lp + 4pL

Combine like terms: -4pL + 4pL = 0
0 = -10L + 3l + -5lp + 4pL

Simplifying
0 = -10L + 3l + -5lp + 4pL

The solution to this equation could not be determined.

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