ln(x-9)=ln(2)+ln(5x)

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Solution for ln(x-9)=ln(2)+ln(5x) equation:


Simplifying
ln(x + -9) = ln(2) + ln(5x)

Reorder the terms:
ln(-9 + x) = ln(2) + ln(5x)
(-9 * ln + x * ln) = ln(2) + ln(5x)
(-9ln + lnx) = ln(2) + ln(5x)

Reorder the terms for easier multiplication:
-9ln + lnx = 2ln + ln(5x)

Remove parenthesis around (5x)
-9ln + lnx = 2ln + ln * 5x

Reorder the terms for easier multiplication:
-9ln + lnx = 2ln + 5ln * x

Multiply ln * x
-9ln + lnx = 2ln + 5lnx

Solving
-9ln + lnx = 2ln + 5lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
-9ln + -2ln + lnx = 2ln + -2ln + 5lnx

Combine like terms: -9ln + -2ln = -11ln
-11ln + lnx = 2ln + -2ln + 5lnx

Combine like terms: 2ln + -2ln = 0
-11ln + lnx = 0 + 5lnx
-11ln + lnx = 5lnx

Add '-5lnx' to each side of the equation.
-11ln + lnx + -5lnx = 5lnx + -5lnx

Combine like terms: lnx + -5lnx = -4lnx
-11ln + -4lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-11ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(11 + 4x) = 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 '(11 + 4x)' equal to zero and attempt to solve: Simplifying 11 + 4x = 0 Solving 11 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 4x = 0 + -11 4x = 0 + -11 Combine like terms: 0 + -11 = -11 4x = -11 Add '-4x' to each side of the equation. 4x + -4x = -11 + -4x Combine like terms: 4x + -4x = 0 0 = -11 + -4x Simplifying 0 = -11 + -4x 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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