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Simplifying loga + log(a + -6) = log(10 + 3a) Reorder the terms: aglo + glo(-6 + a) = log(10 + 3a) aglo + (-6 * glo + a * glo) = log(10 + 3a) Reorder the terms: aglo + (aglo + -6glo) = log(10 + 3a) aglo + (aglo + -6glo) = log(10 + 3a) Combine like terms: aglo + aglo = 2aglo 2aglo + -6glo = log(10 + 3a) 2aglo + -6glo = (10 * glo + 3a * glo) Reorder the terms: 2aglo + -6glo = (3aglo + 10glo) 2aglo + -6glo = (3aglo + 10glo) Solving 2aglo + -6glo = 3aglo + 10glo Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3aglo' to each side of the equation. 2aglo + -3aglo + -6glo = 3aglo + -3aglo + 10glo Combine like terms: 2aglo + -3aglo = -1aglo -1aglo + -6glo = 3aglo + -3aglo + 10glo Combine like terms: 3aglo + -3aglo = 0 -1aglo + -6glo = 0 + 10glo -1aglo + -6glo = 10glo Add '6glo' to each side of the equation. -1aglo + -6glo + 6glo = 10glo + 6glo Combine like terms: -6glo + 6glo = 0 -1aglo + 0 = 10glo + 6glo -1aglo = 10glo + 6glo Combine like terms: 10glo + 6glo = 16glo -1aglo = 16glo Divide each side by '-1glo'. a = -16 Simplifying a = -16
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