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Simplifying ln(4x) + ln(3x) = ln(13) Remove parenthesis around (4x) ln * 4x + ln(3x) = ln(13) Reorder the terms for easier multiplication: 4ln * x + ln(3x) = ln(13) Multiply ln * x 4lnx + ln(3x) = ln(13) Remove parenthesis around (3x) 4lnx + ln * 3x = ln(13) Reorder the terms for easier multiplication: 4lnx + 3ln * x = ln(13) Multiply ln * x 4lnx + 3lnx = ln(13) Combine like terms: 4lnx + 3lnx = 7lnx 7lnx = ln(13) Reorder the terms for easier multiplication: 7lnx = 13ln Solving 7lnx = 13ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. -13ln + 7lnx = 13ln + -13ln Combine like terms: 13ln + -13ln = 0 -13ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 7x) = 0Subproblem 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 '(-13 + 7x)' equal to zero and attempt to solve: Simplifying -13 + 7x = 0 Solving -13 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 7x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 7x = 0 + 13 7x = 0 + 13 Combine like terms: 0 + 13 = 13 7x = 13 Add '-7x' to each side of the equation. 7x + -7x = 13 + -7x Combine like terms: 7x + -7x = 0 0 = 13 + -7x Simplifying 0 = 13 + -7x 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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