ln(3x+1)=ln(2x+8)

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Solution for ln(3x+1)=ln(2x+8) equation:


Simplifying
ln(3x + 1) = ln(2x + 8)

Reorder the terms:
ln(1 + 3x) = ln(2x + 8)
(1 * ln + 3x * ln) = ln(2x + 8)
(1ln + 3lnx) = ln(2x + 8)

Reorder the terms:
1ln + 3lnx = ln(8 + 2x)
1ln + 3lnx = (8 * ln + 2x * ln)
1ln + 3lnx = (8ln + 2lnx)

Solving
1ln + 3lnx = 8ln + 2lnx

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.
1ln + -8ln + 3lnx = 8ln + -8ln + 2lnx

Combine like terms: 1ln + -8ln = -7ln
-7ln + 3lnx = 8ln + -8ln + 2lnx

Combine like terms: 8ln + -8ln = 0
-7ln + 3lnx = 0 + 2lnx
-7ln + 3lnx = 2lnx

Add '-2lnx' to each side of the equation.
-7ln + 3lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 3lnx + -2lnx = 1lnx
-7ln + 1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-7ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + x) = 0

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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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