ln(x-2)=ln(7x)

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Solution for ln(x-2)=ln(7x) equation:


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

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

Remove parenthesis around (7x)
-2ln + lnx = ln * 7x

Reorder the terms for easier multiplication:
-2ln + lnx = 7ln * x

Multiply ln * x
-2ln + lnx = 7lnx

Solving
-2ln + lnx = 7lnx

Solving for variable 'l'.

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

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

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

Combine like terms: 7lnx + -7lnx = 0
-2ln + -6lnx = 0

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