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Simplifying ln(8x) + -1ln(1) = ln(x) + ln(6) Remove parenthesis around (8x) ln * 8x + -1ln(1) = ln(x) + ln(6) Reorder the terms for easier multiplication: 8ln * x + -1ln(1) = ln(x) + ln(6) Multiply ln * x 8lnx + -1ln(1) = ln(x) + ln(6) Reorder the terms for easier multiplication: 8lnx + -1 * 1ln = ln(x) + ln(6) Multiply -1 * 1 8lnx + -1ln = ln(x) + ln(6) Reorder the terms: -1ln + 8lnx = ln(x) + ln(6) Multiply ln * x -1ln + 8lnx = lnx + ln(6) Reorder the terms for easier multiplication: -1ln + 8lnx = lnx + 6ln Reorder the terms: -1ln + 8lnx = 6ln + lnx Solving -1ln + 8lnx = 6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -1ln + -6ln + 8lnx = 6ln + -6ln + lnx Combine like terms: -1ln + -6ln = -7ln -7ln + 8lnx = 6ln + -6ln + lnx Combine like terms: 6ln + -6ln = 0 -7ln + 8lnx = 0 + lnx -7ln + 8lnx = lnx Add '-1lnx' to each side of the equation. -7ln + 8lnx + -1lnx = lnx + -1lnx Combine like terms: 8lnx + -1lnx = 7lnx -7ln + 7lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -7ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(-1 + x) = 0 Ignore the factor 7.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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