ln(y)=ln(x)+ln(x+16)+ln(c)

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Solution for ln(y)=ln(x)+ln(x+16)+ln(c) equation: 


Simplifying
ln(y) = ln(x) + ln(x + 16) + ln(c)

Multiply ln * y
lny = ln(x) + ln(x + 16) + ln(c)

Multiply ln * x
lny = lnx + ln(x + 16) + ln(c)

Reorder the terms:
lny = lnx + ln(16 + x) + ln(c)
lny = lnx + (16 * ln + x * ln) + ln(c)
lny = lnx + (16ln + lnx) + ln(c)

Multiply ln * c
lny = lnx + 16ln + lnx + cln

Reorder the terms:
lny = cln + 16ln + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
lny = cln + 16ln + 2lnx

Solving
lny = cln + 16ln + 2lnx

Solving for variable 'l'.

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

Add '-1cln' to each side of the equation.
-1cln + lny = cln + 16ln + -1cln + 2lnx

Reorder the terms:
-1cln + lny = cln + -1cln + 16ln + 2lnx

Combine like terms: cln + -1cln = 0
-1cln + lny = 0 + 16ln + 2lnx
-1cln + lny = 16ln + 2lnx

Add '-16ln' to each side of the equation.
-1cln + -16ln + lny = 16ln + -16ln + 2lnx

Combine like terms: 16ln + -16ln = 0
-1cln + -16ln + lny = 0 + 2lnx
-1cln + -16ln + lny = 2lnx

Add '-2lnx' to each side of the equation.
-1cln + -16ln + -2lnx + lny = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-1cln + -16ln + -2lnx + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1c + -16 + -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 '(-1c + -16 + -2x + y)' equal to zero and attempt to solve:

Simplifying
-1c + -16 + -2x + y = 0

Reorder the terms:
-16 + -1c + -2x + y = 0

Solving
-16 + -1c + -2x + y = 0

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

Add '16' to each side of the equation.
-16 + -1c + -2x + 16 + y = 0 + 16

Reorder the terms:
-16 + 16 + -1c + -2x + y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1c + -2x + y = 0 + 16
-1c + -2x + y = 0 + 16

Combine like terms: 0 + 16 = 16
-1c + -2x + y = 16

Add 'c' to each side of the equation.
-1c + -2x + c + y = 16 + c

Reorder the terms:
-1c + c + -2x + y = 16 + c

Combine like terms: -1c + c = 0
0 + -2x + y = 16 + c
-2x + y = 16 + c

Add '2x' to each side of the equation.
-2x + 2x + y = 16 + c + 2x

Combine like terms: -2x + 2x = 0
0 + y = 16 + c + 2x
y = 16 + c + 2x

Add '-1y' to each side of the equation.
y + -1y = 16 + c + 2x + -1y

Combine like terms: y + -1y = 0
0 = 16 + c + 2x + -1y

Simplifying
0 = 16 + 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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