ln(x^2)-ln(x^3)+ln(x^5)=ln(16)

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Solution for ln(x^2)-ln(x^3)+ln(x^5)=ln(16) equation: 


Simplifying
ln(x2) + -1ln(x3) + ln(x5) = ln(16)

Multiply ln * x2
lnx2 + -1ln(x3) + ln(x5) = ln(16)

Multiply ln * x3
lnx2 + -1lnx3 + ln(x5) = ln(16)

Multiply ln * x5
lnx2 + -1lnx3 + lnx5 = ln(16)

Reorder the terms for easier multiplication:
lnx2 + -1lnx3 + lnx5 = 16ln

Solving
lnx2 + -1lnx3 + lnx5 = 16ln

Solving for variable 'l'.

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

Add '-16ln' to each side of the equation.
lnx2 + -1lnx3 + -16ln + lnx5 = 16ln + -16ln

Reorder the terms:
-16ln + lnx2 + -1lnx3 + lnx5 = 16ln + -16ln

Combine like terms: 16ln + -16ln = 0
-16ln + lnx2 + -1lnx3 + lnx5 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-16 + x2 + -1x3 + x5) = 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 '(-16 + x2 + -1x3 + x5)' equal to zero and attempt to solve:

Simplifying
-16 + x2 + -1x3 + x5 = 0

Solving
-16 + x2 + -1x3 + x5 = 0

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

Add '16' to each side of the equation.
-16 + x2 + -1x3 + 16 + x5 = 0 + 16

Reorder the terms:
-16 + 16 + x2 + -1x3 + x5 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x2 + -1x3 + x5 = 0 + 16
x2 + -1x3 + x5 = 0 + 16

Combine like terms: 0 + 16 = 16
x2 + -1x3 + x5 = 16

Add '-1x2' to each side of the equation.
x2 + -1x3 + -1x2 + x5 = 16 + -1x2

Reorder the terms:
x2 + -1x2 + -1x3 + x5 = 16 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1x3 + x5 = 16 + -1x2
-1x3 + x5 = 16 + -1x2

Add 'x3' to each side of the equation.
-1x3 + x3 + x5 = 16 + -1x2 + x3

Combine like terms: -1x3 + x3 = 0
0 + x5 = 16 + -1x2 + x3
x5 = 16 + -1x2 + x3

Add '-1x5' to each side of the equation.
x5 + -1x5 = 16 + -1x2 + x3 + -1x5

Combine like terms: x5 + -1x5 = 0
0 = 16 + -1x2 + x3 + -1x5

Simplifying
0 = 16 + -1x2 + x3 + -1x5

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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