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Simplifying ln(30) + ln(x) = 24ln(x + 1) Reorder the terms for easier multiplication: 30ln + ln(x) = 24ln(x + 1) Multiply ln * x 30ln + lnx = 24ln(x + 1) Reorder the terms: 30ln + lnx = 24ln(1 + x) 30ln + lnx = (1 * 24ln + x * 24ln) 30ln + lnx = (24ln + 24lnx) Solving 30ln + lnx = 24ln + 24lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. 30ln + -24ln + lnx = 24ln + -24ln + 24lnx Combine like terms: 30ln + -24ln = 6ln 6ln + lnx = 24ln + -24ln + 24lnx Combine like terms: 24ln + -24ln = 0 6ln + lnx = 0 + 24lnx 6ln + lnx = 24lnx Add '-24lnx' to each side of the equation. 6ln + lnx + -24lnx = 24lnx + -24lnx Combine like terms: lnx + -24lnx = -23lnx 6ln + -23lnx = 24lnx + -24lnx Combine like terms: 24lnx + -24lnx = 0 6ln + -23lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -23x) = 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 '(6 + -23x)' equal to zero and attempt to solve: Simplifying 6 + -23x = 0 Solving 6 + -23x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -23x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -23x = 0 + -6 -23x = 0 + -6 Combine like terms: 0 + -6 = -6 -23x = -6 Add '23x' to each side of the equation. -23x + 23x = -6 + 23x Combine like terms: -23x + 23x = 0 0 = -6 + 23x Simplifying 0 = -6 + 23x 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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