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Simplifying log[4](x + 2) = log[4](3x + -12) Reorder the terms: glo * 4(2 + x) = log[4](3x + -12) Reorder the terms for easier multiplication: 4glo(2 + x) = log[4](3x + -12) (2 * 4glo + x * 4glo) = log[4](3x + -12) (8glo + 4glox) = log[4](3x + -12) Reorder the terms: 8glo + 4glox = glo * 4(-12 + 3x) Reorder the terms for easier multiplication: 8glo + 4glox = 4glo(-12 + 3x) 8glo + 4glox = (-12 * 4glo + 3x * 4glo) 8glo + 4glox = (-48glo + 12glox) Solving 8glo + 4glox = -48glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '48glo' to each side of the equation. 8glo + 48glo + 4glox = -48glo + 48glo + 12glox Combine like terms: 8glo + 48glo = 56glo 56glo + 4glox = -48glo + 48glo + 12glox Combine like terms: -48glo + 48glo = 0 56glo + 4glox = 0 + 12glox 56glo + 4glox = 12glox Add '-12glox' to each side of the equation. 56glo + 4glox + -12glox = 12glox + -12glox Combine like terms: 4glox + -12glox = -8glox 56glo + -8glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 56glo + -8glox = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(7 + -1x) = 0 Ignore the factor 8.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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + 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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