ln(3x)+ln(7x)=ln(22)

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Solution for ln(3x)+ln(7x)=ln(22) equation:


Simplifying
ln(3x) + ln(7x) = ln(22)

Remove parenthesis around (3x)
ln * 3x + ln(7x) = ln(22)

Reorder the terms for easier multiplication:
3ln * x + ln(7x) = ln(22)

Multiply ln * x
3lnx + ln(7x) = ln(22)

Remove parenthesis around (7x)
3lnx + ln * 7x = ln(22)

Reorder the terms for easier multiplication:
3lnx + 7ln * x = ln(22)

Multiply ln * x
3lnx + 7lnx = ln(22)

Combine like terms: 3lnx + 7lnx = 10lnx
10lnx = ln(22)

Reorder the terms for easier multiplication:
10lnx = 22ln

Solving
10lnx = 22ln

Solving for variable 'l'.

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

Add '-22ln' to each side of the equation.
-22ln + 10lnx = 22ln + -22ln

Combine like terms: 22ln + -22ln = 0
-22ln + 10lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-11 + 5x) = 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 '(-11 + 5x)' equal to zero and attempt to solve: Simplifying -11 + 5x = 0 Solving -11 + 5x = 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 + 5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x = 0 + 11 5x = 0 + 11 Combine like terms: 0 + 11 = 11 5x = 11 Add '-5x' to each side of the equation. 5x + -5x = 11 + -5x Combine like terms: 5x + -5x = 0 0 = 11 + -5x Simplifying 0 = 11 + -5x 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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