ln(x)+ln(x+2)=ln(8)

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Solution for ln(x)+ln(x+2)=ln(8) equation:


Simplifying
ln(x) + ln(x + 2) = ln(8)

Multiply ln * x
lnx + ln(x + 2) = ln(8)

Reorder the terms:
lnx + ln(2 + x) = ln(8)
lnx + (2 * ln + x * ln) = ln(8)
lnx + (2ln + lnx) = ln(8)

Reorder the terms:
2ln + lnx + lnx = ln(8)

Combine like terms: lnx + lnx = 2lnx
2ln + 2lnx = ln(8)

Reorder the terms for easier multiplication:
2ln + 2lnx = 8ln

Solving
2ln + 2lnx = 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.
2ln + -8ln + 2lnx = 8ln + -8ln

Combine like terms: 2ln + -8ln = -6ln
-6ln + 2lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-6ln + 2lnx = 0

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

Ignore the factor 2.

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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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