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

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


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

Multiply ln * x
lnx + ln(x + -6) = ln(5x)

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

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

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

Remove parenthesis around (5x)
-6ln + 2lnx = ln * 5x

Reorder the terms for easier multiplication:
-6ln + 2lnx = 5ln * x

Multiply ln * x
-6ln + 2lnx = 5lnx

Solving
-6ln + 2lnx = 5lnx

Solving for variable 'l'.

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

Add '-5lnx' to each side of the equation.
-6ln + 2lnx + -5lnx = 5lnx + -5lnx

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

Combine like terms: 5lnx + -5lnx = 0
-6ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '-3ln'.
-3ln(2 + x) = 0

Ignore the factor -3.

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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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