4ln(x)-3ln(6x)=8ln(7)

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Solution for 4ln(x)-3ln(6x)=8ln(7) equation:


Simplifying
4ln(x) + -3ln(6x) = 8ln(7)

Multiply ln * x
4lnx + -3ln(6x) = 8ln(7)

Remove parenthesis around (6x)
4lnx + -3ln * 6x = 8ln(7)

Reorder the terms for easier multiplication:
4lnx + -3 * 6ln * x = 8ln(7)

Multiply -3 * 6
4lnx + -18ln * x = 8ln(7)

Multiply ln * x
4lnx + -18lnx = 8ln(7)

Combine like terms: 4lnx + -18lnx = -14lnx
-14lnx = 8ln(7)

Reorder the terms for easier multiplication:
-14lnx = 8 * 7ln

Multiply 8 * 7
-14lnx = 56ln

Solving
-14lnx = 56ln

Solving for variable 'l'.

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

Add '-56ln' to each side of the equation.
-56ln + -14lnx = 56ln + -56ln

Combine like terms: 56ln + -56ln = 0
-56ln + -14lnx = 0

Factor out the Greatest Common Factor (GCF), '-14ln'.
-14ln(4 + x) = 0

Ignore the factor -14.

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