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Simplifying In(6) + ln(5x + -10) = ln(11) Reorder the terms for easier multiplication: 6nI + ln(5x + -10) = ln(11) Reorder the terms: 6nI + ln(-10 + 5x) = ln(11) 6nI + (-10 * ln + 5x * ln) = ln(11) 6nI + (-10ln + 5lnx) = ln(11) Reorder the terms: -10ln + 5lnx + 6nI = ln(11) Reorder the terms for easier multiplication: -10ln + 5lnx + 6nI = 11ln Solving -10ln + 5lnx + 6nI = 11ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -10ln + 5lnx + -11ln + 6nI = 11ln + -11ln Reorder the terms: -10ln + -11ln + 5lnx + 6nI = 11ln + -11ln Combine like terms: -10ln + -11ln = -21ln -21ln + 5lnx + 6nI = 11ln + -11ln Combine like terms: 11ln + -11ln = 0 -21ln + 5lnx + 6nI = 0 Add '-6nI' to each side of the equation. -21ln + 5lnx + 6nI + -6nI = 0 + -6nI Combine like terms: 6nI + -6nI = 0 -21ln + 5lnx + 0 = 0 + -6nI -21ln + 5lnx = 0 + -6nI Remove the zero: -21ln + 5lnx = -6nI Combine like terms: -6nI + 6nI = 0 -21ln + 5lnx + 6nI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-21l + 5lx + 6I) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-21l + 5lx + 6I)' equal to zero and attempt to solve: Simplifying -21l + 5lx + 6I = 0 Reorder the terms: 6I + -21l + 5lx = 0 Solving 6I + -21l + 5lx = 0 Move all terms containing l to the left, all other terms to the right. Add '-6I' to each side of the equation. 6I + -21l + -6I + 5lx = 0 + -6I Reorder the terms: 6I + -6I + -21l + 5lx = 0 + -6I Combine like terms: 6I + -6I = 0 0 + -21l + 5lx = 0 + -6I -21l + 5lx = 0 + -6I Remove the zero: -21l + 5lx = -6I 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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