ln(p+q)=ln(p^2)-ln(q)

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Solution for ln(p+q)=ln(p^2)-ln(q) equation: 


Simplifying
ln(p + q) = ln(p2) + -1ln(q)
(p * ln + q * ln) = ln(p2) + -1ln(q)
(lnp + lnq) = ln(p2) + -1ln(q)

Multiply ln * p2
lnp + lnq = lnp2 + -1ln(q)

Multiply ln * q
lnp + lnq = lnp2 + -1lnq

Solving
lnp + lnq = lnp2 + -1lnq

Solving for variable 'l'.

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

Add '-1lnp2' to each side of the equation.
lnp + -1lnp2 + lnq = lnp2 + -1lnp2 + -1lnq

Combine like terms: lnp2 + -1lnp2 = 0
lnp + -1lnp2 + lnq = 0 + -1lnq
lnp + -1lnp2 + lnq = -1lnq

Add 'lnq' to each side of the equation.
lnp + -1lnp2 + lnq + lnq = -1lnq + lnq

Combine like terms: lnq + lnq = 2lnq
lnp + -1lnp2 + 2lnq = -1lnq + lnq

Combine like terms: -1lnq + lnq = 0
lnp + -1lnp2 + 2lnq = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(p + -1p2 + 2q) = 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 '(p + -1p2 + 2q)' equal to zero and attempt to solve:

Simplifying
p + -1p2 + 2q = 0

Solving
p + -1p2 + 2q = 0

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

Add '-1p' to each side of the equation.
p + -1p2 + -1p + 2q = 0 + -1p

Reorder the terms:
p + -1p + -1p2 + 2q = 0 + -1p

Combine like terms: p + -1p = 0
0 + -1p2 + 2q = 0 + -1p
-1p2 + 2q = 0 + -1p
Remove the zero:
-1p2 + 2q = -1p

Add 'p2' to each side of the equation.
-1p2 + p2 + 2q = -1p + p2

Combine like terms: -1p2 + p2 = 0
0 + 2q = -1p + p2
2q = -1p + p2

Add '-2q' to each side of the equation.
2q + -2q = -1p + p2 + -2q

Combine like terms: 2q + -2q = 0
0 = -1p + p2 + -2q

Simplifying
0 = -1p + p2 + -2q

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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