ln(2x-3)+ln(x-2)=2lnz

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Solution for ln(2x-3)+ln(x-2)=2lnz equation:


Simplifying
ln(2x + -3) + ln(x + -2) = 2lnz

Reorder the terms:
ln(-3 + 2x) + ln(x + -2) = 2lnz
(-3 * ln + 2x * ln) + ln(x + -2) = 2lnz
(-3ln + 2lnx) + ln(x + -2) = 2lnz

Reorder the terms:
-3ln + 2lnx + ln(-2 + x) = 2lnz
-3ln + 2lnx + (-2 * ln + x * ln) = 2lnz
-3ln + 2lnx + (-2ln + lnx) = 2lnz

Reorder the terms:
-3ln + -2ln + 2lnx + lnx = 2lnz

Combine like terms: -3ln + -2ln = -5ln
-5ln + 2lnx + lnx = 2lnz

Combine like terms: 2lnx + lnx = 3lnx
-5ln + 3lnx = 2lnz

Solving
-5ln + 3lnx = 2lnz

Solving for variable 'l'.

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

Add '-2lnz' to each side of the equation.
-5ln + 3lnx + -2lnz = 2lnz + -2lnz

Combine like terms: 2lnz + -2lnz = 0
-5ln + 3lnx + -2lnz = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 3x + -2z) = 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 '(-5 + 3x + -2z)' equal to zero and attempt to solve: Simplifying -5 + 3x + -2z = 0 Solving -5 + 3x + -2z = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 3x + 5 + -2z = 0 + 5 Reorder the terms: -5 + 5 + 3x + -2z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x + -2z = 0 + 5 3x + -2z = 0 + 5 Combine like terms: 0 + 5 = 5 3x + -2z = 5 Add '-3x' to each side of the equation. 3x + -3x + -2z = 5 + -3x Combine like terms: 3x + -3x = 0 0 + -2z = 5 + -3x -2z = 5 + -3x Add '2z' to each side of the equation. -2z + 2z = 5 + -3x + 2z Combine like terms: -2z + 2z = 0 0 = 5 + -3x + 2z Simplifying 0 = 5 + -3x + 2z 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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