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Simplifying ln(21x + 4) = ln(10) Reorder the terms: ln(4 + 21x) = ln(10) (4 * ln + 21x * ln) = ln(10) (4ln + 21lnx) = ln(10) Reorder the terms for easier multiplication: 4ln + 21lnx = 10ln Solving 4ln + 21lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 4ln + -10ln + 21lnx = 10ln + -10ln Combine like terms: 4ln + -10ln = -6ln -6ln + 21lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -6ln + 21lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-2 + 7x) = 0 Ignore the factor 3.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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -7x 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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