ln(7x+2)=ln(8)

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Solution for ln(7x+2)=ln(8) equation:


Simplifying
ln(7x + 2) = ln(8)

Reorder the terms:
ln(2 + 7x) = ln(8)
(2 * ln + 7x * ln) = ln(8)
(2ln + 7lnx) = ln(8)

Reorder the terms for easier multiplication:
2ln + 7lnx = 8ln

Solving
2ln + 7lnx = 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 + 7lnx = 8ln + -8ln

Combine like terms: 2ln + -8ln = -6ln
-6ln + 7lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-6ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-6 + 7x) = 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 '(-6 + 7x)' equal to zero and attempt to solve: Simplifying -6 + 7x = 0 Solving -6 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 7x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7x = 0 + 6 7x = 0 + 6 Combine like terms: 0 + 6 = 6 7x = 6 Add '-7x' to each side of the equation. 7x + -7x = 6 + -7x Combine like terms: 7x + -7x = 0 0 = 6 + -7x Simplifying 0 = 6 + -7x 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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