ln(5)+6ln(x)+6ln(x^2+10)=0

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Solution for ln(5)+6ln(x)+6ln(x^2+10)=0 equation:


Simplifying
ln(5) + 6ln(x) + 6ln(x2 + 10) = 0

Reorder the terms for easier multiplication:
5ln + 6ln(x) + 6ln(x2 + 10) = 0

Multiply ln * x
5ln + 6lnx + 6ln(x2 + 10) = 0

Reorder the terms:
5ln + 6lnx + 6ln(10 + x2) = 0
5ln + 6lnx + (10 * 6ln + x2 * 6ln) = 0
5ln + 6lnx + (60ln + 6lnx2) = 0

Reorder the terms:
5ln + 60ln + 6lnx + 6lnx2 = 0

Combine like terms: 5ln + 60ln = 65ln
65ln + 6lnx + 6lnx2 = 0

Solving
65ln + 6lnx + 6lnx2 = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(65 + 6x + 6x2) = 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 '(65 + 6x + 6x2)' equal to zero and attempt to solve: Simplifying 65 + 6x + 6x2 = 0 Solving 65 + 6x + 6x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + 6x + -65 + 6x2 = 0 + -65 Reorder the terms: 65 + -65 + 6x + 6x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + 6x + 6x2 = 0 + -65 6x + 6x2 = 0 + -65 Combine like terms: 0 + -65 = -65 6x + 6x2 = -65 Add '-6x' to each side of the equation. 6x + -6x + 6x2 = -65 + -6x Combine like terms: 6x + -6x = 0 0 + 6x2 = -65 + -6x 6x2 = -65 + -6x Add '-6x2' to each side of the equation. 6x2 + -6x2 = -65 + -6x + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 = -65 + -6x + -6x2 Simplifying 0 = -65 + -6x + -6x2 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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