ln(2x)+ln(x-3)=ln(4)

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Solution for ln(2x)+ln(x-3)=ln(4) equation:


Simplifying
ln(2x) + ln(x + -3) = ln(4)

Remove parenthesis around (2x)
ln * 2x + ln(x + -3) = ln(4)

Reorder the terms for easier multiplication:
2ln * x + ln(x + -3) = ln(4)

Multiply ln * x
2lnx + ln(x + -3) = ln(4)

Reorder the terms:
2lnx + ln(-3 + x) = ln(4)
2lnx + (-3 * ln + x * ln) = ln(4)
2lnx + (-3ln + lnx) = ln(4)

Reorder the terms:
-3ln + 2lnx + lnx = ln(4)

Combine like terms: 2lnx + lnx = 3lnx
-3ln + 3lnx = ln(4)

Reorder the terms for easier multiplication:
-3ln + 3lnx = 4ln

Solving
-3ln + 3lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-3ln + -4ln + 3lnx = 4ln + -4ln

Combine like terms: -3ln + -4ln = -7ln
-7ln + 3lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
-7ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 3x) = 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 '(-7 + 3x)' equal to zero and attempt to solve: Simplifying -7 + 3x = 0 Solving -7 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 0 + 7 3x = 0 + 7 Combine like terms: 0 + 7 = 7 3x = 7 Add '-3x' to each side of the equation. 3x + -3x = 7 + -3x Combine like terms: 3x + -3x = 0 0 = 7 + -3x Simplifying 0 = 7 + -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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