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Simplifying loga(p + 4) = loga(41 + -2p) Reorder the terms: aglo(4 + p) = loga(41 + -2p) (4 * aglo + p * aglo) = loga(41 + -2p) (4aglo + aglop) = loga(41 + -2p) 4aglo + aglop = (41 * aglo + -2p * aglo) 4aglo + aglop = (41aglo + -2aglop) Solving 4aglo + aglop = 41aglo + -2aglop Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-41aglo' to each side of the equation. 4aglo + -41aglo + aglop = 41aglo + -41aglo + -2aglop Combine like terms: 4aglo + -41aglo = -37aglo -37aglo + aglop = 41aglo + -41aglo + -2aglop Combine like terms: 41aglo + -41aglo = 0 -37aglo + aglop = 0 + -2aglop -37aglo + aglop = -2aglop Add '2aglop' to each side of the equation. -37aglo + aglop + 2aglop = -2aglop + 2aglop Combine like terms: aglop + 2aglop = 3aglop -37aglo + 3aglop = -2aglop + 2aglop Combine like terms: -2aglop + 2aglop = 0 -37aglo + 3aglop = 0 Factor out the Greatest Common Factor (GCF), 'aglo'. aglo(-37 + 3p) = 0Subproblem 1
Set the factor 'aglo' equal to zero and attempt to solve: Simplifying aglo = 0 Solving aglo = 0 Move all terms containing a to the left, all other terms to the right. Simplifying aglo = 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 '(-37 + 3p)' equal to zero and attempt to solve: Simplifying -37 + 3p = 0 Solving -37 + 3p = 0 Move all terms containing a to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + 3p = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 3p = 0 + 37 3p = 0 + 37 Combine like terms: 0 + 37 = 37 3p = 37 Add '-3p' to each side of the equation. 3p + -3p = 37 + -3p Combine like terms: 3p + -3p = 0 0 = 37 + -3p Simplifying 0 = 37 + -3p 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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