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Simplifying ln(x + 4) = 10ln(10x) Reorder the terms: ln(4 + x) = 10ln(10x) (4 * ln + x * ln) = 10ln(10x) (4ln + lnx) = 10ln(10x) Remove parenthesis around (10x) 4ln + lnx = 10ln * 10x Reorder the terms for easier multiplication: 4ln + lnx = 10 * 10ln * x Multiply 10 * 10 4ln + lnx = 100ln * x Multiply ln * x 4ln + lnx = 100lnx Solving 4ln + lnx = 100lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-100lnx' to each side of the equation. 4ln + lnx + -100lnx = 100lnx + -100lnx Combine like terms: lnx + -100lnx = -99lnx 4ln + -99lnx = 100lnx + -100lnx Combine like terms: 100lnx + -100lnx = 0 4ln + -99lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + -99x) = 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 '(4 + -99x)' equal to zero and attempt to solve: Simplifying 4 + -99x = 0 Solving 4 + -99x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -99x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -99x = 0 + -4 -99x = 0 + -4 Combine like terms: 0 + -4 = -4 -99x = -4 Add '99x' to each side of the equation. -99x + 99x = -4 + 99x Combine like terms: -99x + 99x = 0 0 = -4 + 99x Simplifying 0 = -4 + 99x 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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