ln(x)+ln(x-5)-ln(7x)=ln(7)

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Solution for ln(x)+ln(x-5)-ln(7x)=ln(7) equation:


Simplifying
ln(x) + ln(x + -5) + -1ln(7x) = ln(7)

Multiply ln * x
lnx + ln(x + -5) + -1ln(7x) = ln(7)

Reorder the terms:
lnx + ln(-5 + x) + -1ln(7x) = ln(7)
lnx + (-5 * ln + x * ln) + -1ln(7x) = ln(7)
lnx + (-5ln + lnx) + -1ln(7x) = ln(7)

Remove parenthesis around (7x)
lnx + -5ln + lnx + -1ln * 7x = ln(7)

Reorder the terms for easier multiplication:
lnx + -5ln + lnx + -1 * 7ln * x = ln(7)

Multiply -1 * 7
lnx + -5ln + lnx + -7ln * x = ln(7)

Multiply ln * x
lnx + -5ln + lnx + -7lnx = ln(7)

Reorder the terms:
-5ln + lnx + lnx + -7lnx = ln(7)

Combine like terms: lnx + lnx = 2lnx
-5ln + 2lnx + -7lnx = ln(7)

Combine like terms: 2lnx + -7lnx = -5lnx
-5ln + -5lnx = ln(7)

Reorder the terms for easier multiplication:
-5ln + -5lnx = 7ln

Solving
-5ln + -5lnx = 7ln

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
-5ln + -7ln + -5lnx = 7ln + -7ln

Combine like terms: -5ln + -7ln = -12ln
-12ln + -5lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
-12ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(12 + 5x) = 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 '(12 + 5x)' equal to zero and attempt to solve: Simplifying 12 + 5x = 0 Solving 12 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5x = 0 + -12 5x = 0 + -12 Combine like terms: 0 + -12 = -12 5x = -12 Add '-5x' to each side of the equation. 5x + -5x = -12 + -5x Combine like terms: 5x + -5x = 0 0 = -12 + -5x Simplifying 0 = -12 + -5x 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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