ln(y)=ln(x)+ln(x+13)+ln(C)

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Solution for ln(y)=ln(x)+ln(x+13)+ln(C) equation: 


Simplifying
ln(y) = ln(x) + ln(x + 13) + ln(C)

Multiply ln * y
lny = ln(x) + ln(x + 13) + ln(C)

Multiply ln * x
lny = lnx + ln(x + 13) + ln(C)

Reorder the terms:
lny = lnx + ln(13 + x) + ln(C)
lny = lnx + (13 * ln + x * ln) + ln(C)
lny = lnx + (13ln + lnx) + ln(C)

Multiply ln * C
lny = lnx + 13ln + lnx + lnC

Reorder the terms:
lny = 13ln + lnC + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
lny = 13ln + lnC + 2lnx

Solving
lny = 13ln + lnC + 2lnx

Solving for variable 'l'.

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

Add '-13ln' to each side of the equation.
-13ln + lny = 13ln + lnC + -13ln + 2lnx

Reorder the terms:
-13ln + lny = 13ln + -13ln + lnC + 2lnx

Combine like terms: 13ln + -13ln = 0
-13ln + lny = 0 + lnC + 2lnx
-13ln + lny = lnC + 2lnx

Add '-1lnC' to each side of the equation.
-13ln + -1lnC + lny = lnC + -1lnC + 2lnx

Combine like terms: lnC + -1lnC = 0
-13ln + -1lnC + lny = 0 + 2lnx
-13ln + -1lnC + lny = 2lnx

Add '-2lnx' to each side of the equation.
-13ln + -1lnC + -2lnx + lny = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-13ln + -1lnC + -2lnx + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-13 + -1C + -2x + y) = 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 '(-13 + -1C + -2x + y)' equal to zero and attempt to solve:

Simplifying
-13 + -1C + -2x + y = 0

Solving
-13 + -1C + -2x + y = 0

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

Add '13' to each side of the equation.
-13 + -1C + -2x + 13 + y = 0 + 13

Reorder the terms:
-13 + 13 + -1C + -2x + y = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1C + -2x + y = 0 + 13
-1C + -2x + y = 0 + 13

Combine like terms: 0 + 13 = 13
-1C + -2x + y = 13

Add 'C' to each side of the equation.
-1C + -2x + C + y = 13 + C

Reorder the terms:
-1C + C + -2x + y = 13 + C

Combine like terms: -1C + C = 0
0 + -2x + y = 13 + C
-2x + y = 13 + C

Add '2x' to each side of the equation.
-2x + 2x + y = 13 + C + 2x

Combine like terms: -2x + 2x = 0
0 + y = 13 + C + 2x
y = 13 + C + 2x

Add '-1y' to each side of the equation.
y + -1y = 13 + C + 2x + -1y

Combine like terms: y + -1y = 0
0 = 13 + C + 2x + -1y

Simplifying
0 = 13 + C + 2x + -1y

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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