x=ln(5x^3)+ln(x)

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

Simplifying
x = ln(5x3) + ln(x)

Remove parenthesis around (5x3)
x = ln * 5x3 + ln(x)

Reorder the terms for easier multiplication:
x = 5ln * x3 + ln(x)

Multiply ln * x3
x = 5lnx3 + ln(x)

Multiply ln * x
x = 5lnx3 + lnx

Reorder the terms:
x = lnx + 5lnx3

Solving
x = lnx + 5lnx3

Solving for variable 'x'.

Reorder the terms:
-1lnx + -5lnx3 + x = lnx + 5lnx3 + -1lnx + -5lnx3

Reorder the terms:
-1lnx + -5lnx3 + x = lnx + -1lnx + 5lnx3 + -5lnx3

Combine like terms: lnx + -1lnx = 0
-1lnx + -5lnx3 + x = 0 + 5lnx3 + -5lnx3
-1lnx + -5lnx3 + x = 5lnx3 + -5lnx3

Combine like terms: 5lnx3 + -5lnx3 = 0
-1lnx + -5lnx3 + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ln + -5lnx2 + 1) = 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 '(-1ln + -5lnx2 + 1)' equal to zero and attempt to solve:

Simplifying
-1ln + -5lnx2 + 1 = 0

Reorder the terms:
1 + -1ln + -5lnx2 = 0

Solving
1 + -1ln + -5lnx2 = 0

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

Add '-1' to each side of the equation.
1 + -1ln + -1 + -5lnx2 = 0 + -1

Reorder the terms:
1 + -1 + -1ln + -5lnx2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1ln + -5lnx2 = 0 + -1
-1ln + -5lnx2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1ln + -5lnx2 = -1

Add 'ln' to each side of the equation.
-1ln + ln + -5lnx2 = -1 + ln

Combine like terms: -1ln + ln = 0
0 + -5lnx2 = -1 + ln
-5lnx2 = -1 + ln

Divide each side by '-5ln'.
x2 = 0.2l-1n-1 + -0.2

Simplifying
x2 = 0.2l-1n-1 + -0.2

Reorder the terms:
x2 = -0.2 + 0.2l-1n-1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}