ln(x+5)+ln(x^2)=ln(x*6)

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Solution for ln(x+5)+ln(x^2)=ln(x*6) equation: 


Simplifying
ln(x + 5) + ln(x2) = ln(x * 6)

Reorder the terms:
ln(5 + x) + ln(x2) = ln(x * 6)
(5 * ln + x * ln) + ln(x2) = ln(x * 6)
(5ln + lnx) + ln(x2) = ln(x * 6)

Multiply ln * x2
5ln + lnx + lnx2 = ln(x * 6)

Reorder the terms for easier multiplication:
5ln + lnx + lnx2 = ln(6x)

Remove parenthesis around (6x)
5ln + lnx + lnx2 = ln * 6x

Reorder the terms for easier multiplication:
5ln + lnx + lnx2 = 6ln * x

Multiply ln * x
5ln + lnx + lnx2 = 6lnx

Solving
5ln + lnx + lnx2 = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
5ln + lnx + -6lnx + lnx2 = 6lnx + -6lnx

Combine like terms: lnx + -6lnx = -5lnx
5ln + -5lnx + lnx2 = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
5ln + -5lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -5x + x2) = 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 '(5 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -5x + x2 = 0

Solving
5 + -5x + x2 = 0

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

Add '-5' to each side of the equation.
5 + -5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5x + x2 = 0 + -5
-5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5x + x2 = -5

Add '5x' to each side of the equation.
-5x + 5x + x2 = -5 + 5x

Combine like terms: -5x + 5x = 0
0 + x2 = -5 + 5x
x2 = -5 + 5x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -5 + 5x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -5 + 5x + -1x2

Simplifying
0 = -5 + 5x + -1x2

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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