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Simplifying ln(6x) + ln(2x) = ln(13) Remove parenthesis around (6x) ln * 6x + ln(2x) = ln(13) Reorder the terms for easier multiplication: 6ln * x + ln(2x) = ln(13) Multiply ln * x 6lnx + ln(2x) = ln(13) Remove parenthesis around (2x) 6lnx + ln * 2x = ln(13) Reorder the terms for easier multiplication: 6lnx + 2ln * x = ln(13) Multiply ln * x 6lnx + 2lnx = ln(13) Combine like terms: 6lnx + 2lnx = 8lnx 8lnx = ln(13) Reorder the terms for easier multiplication: 8lnx = 13ln Solving 8lnx = 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 + 8lnx = 13ln + -13ln Combine like terms: 13ln + -13ln = 0 -13ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 8x) = 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 + 8x)' equal to zero and attempt to solve: Simplifying -13 + 8x = 0 Solving -13 + 8x = 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 + 8x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 8x = 0 + 13 8x = 0 + 13 Combine like terms: 0 + 13 = 13 8x = 13 Add '-8x' to each side of the equation. 8x + -8x = 13 + -8x Combine like terms: 8x + -8x = 0 0 = 13 + -8x Simplifying 0 = 13 + -8x 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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