3ln(2)+ln(8)=2ln(4x)

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Solution for 3ln(2)+ln(8)=2ln(4x) equation:


Simplifying
3ln(2) + ln(8) = 2ln(4x)

Reorder the terms for easier multiplication:
3 * 2ln + ln(8) = 2ln(4x)

Multiply 3 * 2
6ln + ln(8) = 2ln(4x)

Reorder the terms for easier multiplication:
6ln + 8ln = 2ln(4x)

Combine like terms: 6ln + 8ln = 14ln
14ln = 2ln(4x)

Remove parenthesis around (4x)
14ln = 2ln * 4x

Reorder the terms for easier multiplication:
14ln = 2 * 4ln * x

Multiply 2 * 4
14ln = 8ln * x

Multiply ln * x
14ln = 8lnx

Solving
14ln = 8lnx

Solving for variable 'l'.

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

Add '-8lnx' to each side of the equation.
14ln + -8lnx = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
14ln + -8lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(7 + -4x) = 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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Add '4x' to each side of the equation. -4x + 4x = -7 + 4x Combine like terms: -4x + 4x = 0 0 = -7 + 4x Simplifying 0 = -7 + 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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