ln(x-1)+ln(x-2)=ln(8x+28)

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Solution for ln(x-1)+ln(x-2)=ln(8x+28) equation:


Simplifying
ln(x + -1) + ln(x + -2) = ln(8x + 28)

Reorder the terms:
ln(-1 + x) + ln(x + -2) = ln(8x + 28)
(-1 * ln + x * ln) + ln(x + -2) = ln(8x + 28)
(-1ln + lnx) + ln(x + -2) = ln(8x + 28)

Reorder the terms:
-1ln + lnx + ln(-2 + x) = ln(8x + 28)
-1ln + lnx + (-2 * ln + x * ln) = ln(8x + 28)
-1ln + lnx + (-2ln + lnx) = ln(8x + 28)

Reorder the terms:
-1ln + -2ln + lnx + lnx = ln(8x + 28)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lnx + lnx = ln(8x + 28)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(8x + 28)

Reorder the terms:
-3ln + 2lnx = ln(28 + 8x)
-3ln + 2lnx = (28 * ln + 8x * ln)
-3ln + 2lnx = (28ln + 8lnx)

Solving
-3ln + 2lnx = 28ln + 8lnx

Solving for variable 'l'.

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

Add '-28ln' to each side of the equation.
-3ln + -28ln + 2lnx = 28ln + -28ln + 8lnx

Combine like terms: -3ln + -28ln = -31ln
-31ln + 2lnx = 28ln + -28ln + 8lnx

Combine like terms: 28ln + -28ln = 0
-31ln + 2lnx = 0 + 8lnx
-31ln + 2lnx = 8lnx

Add '-8lnx' to each side of the equation.
-31ln + 2lnx + -8lnx = 8lnx + -8lnx

Combine like terms: 2lnx + -8lnx = -6lnx
-31ln + -6lnx = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
-31ln + -6lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(31 + 6x) = 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 '(31 + 6x)' equal to zero and attempt to solve: Simplifying 31 + 6x = 0 Solving 31 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 6x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 6x = 0 + -31 6x = 0 + -31 Combine like terms: 0 + -31 = -31 6x = -31 Add '-6x' to each side of the equation. 6x + -6x = -31 + -6x Combine like terms: 6x + -6x = 0 0 = -31 + -6x Simplifying 0 = -31 + -6x 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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