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Simplifying Ln(6x) + ln(3x) = ln(19) Remove parenthesis around (6x) nL * 6x + ln(3x) = ln(19) Reorder the terms for easier multiplication: 6nL * x + ln(3x) = ln(19) Multiply nL * x 6nxL + ln(3x) = ln(19) Remove parenthesis around (3x) 6nxL + ln * 3x = ln(19) Reorder the terms for easier multiplication: 6nxL + 3ln * x = ln(19) Multiply ln * x 6nxL + 3lnx = ln(19) Reorder the terms: 3lnx + 6nxL = ln(19) Reorder the terms for easier multiplication: 3lnx + 6nxL = 19ln Solving 3lnx + 6nxL = 19ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-19ln' to each side of the equation. 3lnx + -19ln + 6nxL = 19ln + -19ln Reorder the terms: -19ln + 3lnx + 6nxL = 19ln + -19ln Combine like terms: 19ln + -19ln = 0 -19ln + 3lnx + 6nxL = 0 Add '-6nxL' to each side of the equation. -19ln + 3lnx + 6nxL + -6nxL = 0 + -6nxL Combine like terms: 6nxL + -6nxL = 0 -19ln + 3lnx + 0 = 0 + -6nxL -19ln + 3lnx = 0 + -6nxL Remove the zero: -19ln + 3lnx = -6nxL Combine like terms: -6nxL + 6nxL = 0 -19ln + 3lnx + 6nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-19l + 3lx + 6xL) = 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 '(-19l + 3lx + 6xL)' equal to zero and attempt to solve: Simplifying -19l + 3lx + 6xL = 0 Solving -19l + 3lx + 6xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-6xL' to each side of the equation. -19l + 3lx + 6xL + -6xL = 0 + -6xL Combine like terms: 6xL + -6xL = 0 -19l + 3lx + 0 = 0 + -6xL -19l + 3lx = 0 + -6xL Remove the zero: -19l + 3lx = -6xL 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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