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Simplifying ln(x + -4) + ln(5x) = ln(25) Reorder the terms: ln(-4 + x) + ln(5x) = ln(25) (-4 * ln + x * ln) + ln(5x) = ln(25) (-4ln + lnx) + ln(5x) = ln(25) Remove parenthesis around (5x) -4ln + lnx + ln * 5x = ln(25) Reorder the terms for easier multiplication: -4ln + lnx + 5ln * x = ln(25) Multiply ln * x -4ln + lnx + 5lnx = ln(25) Combine like terms: lnx + 5lnx = 6lnx -4ln + 6lnx = ln(25) Reorder the terms for easier multiplication: -4ln + 6lnx = 25ln Solving -4ln + 6lnx = 25ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. -4ln + -25ln + 6lnx = 25ln + -25ln Combine like terms: -4ln + -25ln = -29ln -29ln + 6lnx = 25ln + -25ln Combine like terms: 25ln + -25ln = 0 -29ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-29 + 6x) = 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 '(-29 + 6x)' equal to zero and attempt to solve: Simplifying -29 + 6x = 0 Solving -29 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + 6x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 6x = 0 + 29 6x = 0 + 29 Combine like terms: 0 + 29 = 29 6x = 29 Add '-6x' to each side of the equation. 6x + -6x = 29 + -6x Combine like terms: 6x + -6x = 0 0 = 29 + -6x Simplifying 0 = 29 + -6x 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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