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Simplifying 2log[4](6) + log[4](2x + 3) = log[4](8x + -14) Reorder the terms for easier multiplication: 2 * 4 * 6glo + log[4](2x + 3) = log[4](8x + -14) Multiply 2 * 4 8 * 6glo + log[4](2x + 3) = log[4](8x + -14) Multiply 8 * 6 48glo + log[4](2x + 3) = log[4](8x + -14) Reorder the terms: 48glo + glo * 4(3 + 2x) = log[4](8x + -14) Reorder the terms for easier multiplication: 48glo + 4glo(3 + 2x) = log[4](8x + -14) 48glo + (3 * 4glo + 2x * 4glo) = log[4](8x + -14) 48glo + (12glo + 8glox) = log[4](8x + -14) Combine like terms: 48glo + 12glo = 60glo 60glo + 8glox = log[4](8x + -14) Reorder the terms: 60glo + 8glox = glo * 4(-14 + 8x) Reorder the terms for easier multiplication: 60glo + 8glox = 4glo(-14 + 8x) 60glo + 8glox = (-14 * 4glo + 8x * 4glo) 60glo + 8glox = (-56glo + 32glox) Solving 60glo + 8glox = -56glo + 32glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '56glo' to each side of the equation. 60glo + 56glo + 8glox = -56glo + 56glo + 32glox Combine like terms: 60glo + 56glo = 116glo 116glo + 8glox = -56glo + 56glo + 32glox Combine like terms: -56glo + 56glo = 0 116glo + 8glox = 0 + 32glox 116glo + 8glox = 32glox Add '-32glox' to each side of the equation. 116glo + 8glox + -32glox = 32glox + -32glox Combine like terms: 8glox + -32glox = -24glox 116glo + -24glox = 32glox + -32glox Combine like terms: 32glox + -32glox = 0 116glo + -24glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(29 + -6x) = 0 Ignore the factor 4.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 '(29 + -6x)' equal to zero and attempt to solve: Simplifying 29 + -6x = 0 Solving 29 + -6x = 0 Move all terms containing g to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -6x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -6x = 0 + -29 -6x = 0 + -29 Combine like terms: 0 + -29 = -29 -6x = -29 Add '6x' to each side of the equation. -6x + 6x = -29 + 6x Combine like terms: -6x + 6x = 0 0 = -29 + 6x Simplifying 0 = -29 + 6x 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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