F(x)=e^5xln(x)

Solution for F(x)=e^5xln(x) equation:

Simplifying
F(x) = e5xln(x)

Multiply F * x
xF = e5xln(x)

Multiply e5lnx * x
xF = e5lnx2

Solving
xF = e5lnx2

Solving for variable 'x'.

Reorder the terms:
-1e5lnx2 + xF = e5lnx2 + -1e5lnx2

Combine like terms: e5lnx2 + -1e5lnx2 = 0
-1e5lnx2 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1e5lnx + F) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1e5lnx + F)' equal to zero and attempt to solve:

Simplifying
-1e5lnx + F = 0

Reorder the terms:
F + -1e5lnx = 0

Solving
F + -1e5lnx = 0

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

Add '-1F' to each side of the equation.
F + -1F + -1e5lnx = 0 + -1F

Combine like terms: F + -1F = 0
0 + -1e5lnx = 0 + -1F
-1e5lnx = 0 + -1F
Remove the zero:
-1e5lnx = -1F

Divide each side by '-1e5ln'.
x = e-5l-1n-1F

Simplifying
x = e-5l-1n-1F
Solution
x = {0, e-5l-1n-1F}