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Simplifying loga(486) = loga(3x) + 4loga(6) Reorder the terms for easier multiplication: 486aglo = loga(3x) + 4loga(6) Remove parenthesis around (3x) 486aglo = aglo * 3x + 4loga(6) Reorder the terms for easier multiplication: 486aglo = 3aglo * x + 4loga(6) Multiply aglo * x 486aglo = 3aglox + 4loga(6) Reorder the terms for easier multiplication: 486aglo = 3aglox + 4 * 6aglo Multiply 4 * 6 486aglo = 3aglox + 24aglo Reorder the terms: 486aglo = 24aglo + 3aglox Solving 486aglo = 24aglo + 3aglox Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-24aglo' to each side of the equation. 486aglo + -24aglo = 24aglo + -24aglo + 3aglox Combine like terms: 486aglo + -24aglo = 462aglo 462aglo = 24aglo + -24aglo + 3aglox Combine like terms: 24aglo + -24aglo = 0 462aglo = 0 + 3aglox 462aglo = 3aglox Add '-3aglox' to each side of the equation. 462aglo + -3aglox = 3aglox + -3aglox Combine like terms: 3aglox + -3aglox = 0 462aglo + -3aglox = 0 Factor out the Greatest Common Factor (GCF), '3aglo'. 3aglo(154 + -1x) = 0 Ignore the factor 3.Subproblem 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 '(154 + -1x)' equal to zero and attempt to solve: Simplifying 154 + -1x = 0 Solving 154 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-154' to each side of the equation. 154 + -154 + -1x = 0 + -154 Combine like terms: 154 + -154 = 0 0 + -1x = 0 + -154 -1x = 0 + -154 Combine like terms: 0 + -154 = -154 -1x = -154 Add 'x' to each side of the equation. -1x + x = -154 + x Combine like terms: -1x + x = 0 0 = -154 + x Simplifying 0 = -154 + x 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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