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Simplifying ln(x) + ln(x + 4) = ln(15) + ln(3) Multiply ln * x lnx + ln(x + 4) = ln(15) + ln(3) Reorder the terms: lnx + ln(4 + x) = ln(15) + ln(3) lnx + (4 * ln + x * ln) = ln(15) + ln(3) lnx + (4ln + lnx) = ln(15) + ln(3) Reorder the terms: 4ln + lnx + lnx = ln(15) + ln(3) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(15) + ln(3) Reorder the terms for easier multiplication: 4ln + 2lnx = 15ln + ln(3) Reorder the terms for easier multiplication: 4ln + 2lnx = 15ln + 3ln Combine like terms: 15ln + 3ln = 18ln 4ln + 2lnx = 18ln Solving 4ln + 2lnx = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 4ln + -18ln + 2lnx = 18ln + -18ln Combine like terms: 4ln + -18ln = -14ln -14ln + 2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -14ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-7 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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