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Simplifying log[12](2m + 7) = log[12](2 + -3m) Reorder the terms: glo * 12(7 + 2m) = log[12](2 + -3m) Reorder the terms for easier multiplication: 12glo(7 + 2m) = log[12](2 + -3m) (7 * 12glo + 2m * 12glo) = log[12](2 + -3m) Reorder the terms: (24glmo + 84glo) = log[12](2 + -3m) (24glmo + 84glo) = log[12](2 + -3m) Reorder the terms for easier multiplication: 24glmo + 84glo = 12glo(2 + -3m) 24glmo + 84glo = (2 * 12glo + -3m * 12glo) Reorder the terms: 24glmo + 84glo = (-36glmo + 24glo) 24glmo + 84glo = (-36glmo + 24glo) Solving 24glmo + 84glo = -36glmo + 24glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '36glmo' to each side of the equation. 24glmo + 36glmo + 84glo = -36glmo + 36glmo + 24glo Combine like terms: 24glmo + 36glmo = 60glmo 60glmo + 84glo = -36glmo + 36glmo + 24glo Combine like terms: -36glmo + 36glmo = 0 60glmo + 84glo = 0 + 24glo 60glmo + 84glo = 24glo Add '-24glo' to each side of the equation. 60glmo + 84glo + -24glo = 24glo + -24glo Combine like terms: 84glo + -24glo = 60glo 60glmo + 60glo = 24glo + -24glo Combine like terms: 24glo + -24glo = 0 60glmo + 60glo = 0 Factor out the Greatest Common Factor (GCF), '60glo'. 60glo(m + 1) = 0 Ignore the factor 60.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(m + 1)' equal to zero and attempt to solve: Simplifying m + 1 = 0 Reorder the terms: 1 + m = 0 Solving 1 + m = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0 + -1 m = 0 + -1 Combine like terms: 0 + -1 = -1 m = -1 Add '-1m' to each side of the equation. m + -1m = -1 + -1m Combine like terms: m + -1m = 0 0 = -1 + -1m Simplifying 0 = -1 + -1m 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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