ln(7x+11)-ln(x)=ln(8)

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Solution for ln(7x+11)-ln(x)=ln(8) equation:


Simplifying
ln(7x + 11) + -1ln(x) = ln(8)

Reorder the terms:
ln(11 + 7x) + -1ln(x) = ln(8)
(11 * ln + 7x * ln) + -1ln(x) = ln(8)
(11ln + 7lnx) + -1ln(x) = ln(8)

Multiply ln * x
11ln + 7lnx + -1lnx = ln(8)

Combine like terms: 7lnx + -1lnx = 6lnx
11ln + 6lnx = ln(8)

Reorder the terms for easier multiplication:
11ln + 6lnx = 8ln

Solving
11ln + 6lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
11ln + -8ln + 6lnx = 8ln + -8ln

Combine like terms: 11ln + -8ln = 3ln
3ln + 6lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
3ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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