ln(x+2)+ln(x-5)=ln(6x)

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


Simplifying
ln(x + 2) + ln(x + -5) = ln(6x)

Reorder the terms:
ln(2 + x) + ln(x + -5) = ln(6x)
(2 * ln + x * ln) + ln(x + -5) = ln(6x)
(2ln + lnx) + ln(x + -5) = ln(6x)

Reorder the terms:
2ln + lnx + ln(-5 + x) = ln(6x)
2ln + lnx + (-5 * ln + x * ln) = ln(6x)
2ln + lnx + (-5ln + lnx) = ln(6x)

Reorder the terms:
2ln + -5ln + lnx + lnx = ln(6x)

Combine like terms: 2ln + -5ln = -3ln
-3ln + lnx + lnx = ln(6x)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(6x)

Remove parenthesis around (6x)
-3ln + 2lnx = ln * 6x

Reorder the terms for easier multiplication:
-3ln + 2lnx = 6ln * x

Multiply ln * x
-3ln + 2lnx = 6lnx

Solving
-3ln + 2lnx = 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.
-3ln + 2lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 2lnx + -6lnx = -4lnx
-3ln + -4lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-3ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(3 + 4x) = 0

Ignore the factor -1.

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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Add '-4x' to each side of the equation. 4x + -4x = -3 + -4x Combine like terms: 4x + -4x = 0 0 = -3 + -4x Simplifying 0 = -3 + -4x 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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