lny^3=ln(x^5*e^2)

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Solution for lny^3=ln(x^5*e^2) equation: 


Simplifying
lny3 = ln(x5 * e2)

Multiply x5 * e2
lny3 = ln(e2x5)

Multiply ln * e2x5
lny3 = e2lnx5

Solving
lny3 = e2lnx5

Solving for variable 'l'.

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

Add '-1e2lnx5' to each side of the equation.
-1e2lnx5 + lny3 = e2lnx5 + -1e2lnx5

Combine like terms: e2lnx5 + -1e2lnx5 = 0
-1e2lnx5 + lny3 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1e2x5 + y3) = 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 '(-1e2x5 + y3)' equal to zero and attempt to solve:

Simplifying
-1e2x5 + y3 = 0

Solving
-1e2x5 + y3 = 0

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

Add 'e2x5' to each side of the equation.
-1e2x5 + e2x5 + y3 = 0 + e2x5

Combine like terms: -1e2x5 + e2x5 = 0
0 + y3 = 0 + e2x5
y3 = 0 + e2x5
Remove the zero:
y3 = e2x5

Add '-1y3' to each side of the equation.
y3 + -1y3 = e2x5 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = e2x5 + -1y3

Simplifying
0 = e2x5 + -1y3

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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