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Simplifying ln(5p + 10) = ln(3p + 1) Reorder the terms: ln(10 + 5p) = ln(3p + 1) (10 * ln + 5p * ln) = ln(3p + 1) (10ln + 5lnp) = ln(3p + 1) Reorder the terms: 10ln + 5lnp = ln(1 + 3p) 10ln + 5lnp = (1 * ln + 3p * ln) 10ln + 5lnp = (1ln + 3lnp) Solving 10ln + 5lnp = 1ln + 3lnp Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 10ln + -1ln + 5lnp = 1ln + -1ln + 3lnp Combine like terms: 10ln + -1ln = 9ln 9ln + 5lnp = 1ln + -1ln + 3lnp Combine like terms: 1ln + -1ln = 0 9ln + 5lnp = 0 + 3lnp 9ln + 5lnp = 3lnp Add '-3lnp' to each side of the equation. 9ln + 5lnp + -3lnp = 3lnp + -3lnp Combine like terms: 5lnp + -3lnp = 2lnp 9ln + 2lnp = 3lnp + -3lnp Combine like terms: 3lnp + -3lnp = 0 9ln + 2lnp = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 2p) = 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 '(9 + 2p)' equal to zero and attempt to solve: Simplifying 9 + 2p = 0 Solving 9 + 2p = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2p = 0 + -9 2p = 0 + -9 Combine like terms: 0 + -9 = -9 2p = -9 Add '-2p' to each side of the equation. 2p + -2p = -9 + -2p Combine like terms: 2p + -2p = 0 0 = -9 + -2p Simplifying 0 = -9 + -2p 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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