ln(5x-2)+ln(4x)=2lnx

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Solution for ln(5x-2)+ln(4x)=2lnx equation:


Simplifying
ln(5x + -2) + ln(4x) = 2lnx

Reorder the terms:
ln(-2 + 5x) + ln(4x) = 2lnx
(-2 * ln + 5x * ln) + ln(4x) = 2lnx
(-2ln + 5lnx) + ln(4x) = 2lnx

Remove parenthesis around (4x)
-2ln + 5lnx + ln * 4x = 2lnx

Reorder the terms for easier multiplication:
-2ln + 5lnx + 4ln * x = 2lnx

Multiply ln * x
-2ln + 5lnx + 4lnx = 2lnx

Combine like terms: 5lnx + 4lnx = 9lnx
-2ln + 9lnx = 2lnx

Solving
-2ln + 9lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
-2ln + 9lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 9lnx + -2lnx = 7lnx
-2ln + 7lnx = 2lnx + -2lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -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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