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Simplifying log[4](x) + log[4](x + -3) = log[4](-7x + 21) Reorder the terms for easier multiplication: 4glo * x + log[4](x + -3) = log[4](-7x + 21) Multiply glo * x 4glox + log[4](x + -3) = log[4](-7x + 21) Reorder the terms: 4glox + glo * 4(-3 + x) = log[4](-7x + 21) Reorder the terms for easier multiplication: 4glox + 4glo(-3 + x) = log[4](-7x + 21) 4glox + (-3 * 4glo + x * 4glo) = log[4](-7x + 21) 4glox + (-12glo + 4glox) = log[4](-7x + 21) Reorder the terms: -12glo + 4glox + 4glox = log[4](-7x + 21) Combine like terms: 4glox + 4glox = 8glox -12glo + 8glox = log[4](-7x + 21) Reorder the terms: -12glo + 8glox = glo * 4(21 + -7x) Reorder the terms for easier multiplication: -12glo + 8glox = 4glo(21 + -7x) -12glo + 8glox = (21 * 4glo + -7x * 4glo) -12glo + 8glox = (84glo + -28glox) Solving -12glo + 8glox = 84glo + -28glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-84glo' to each side of the equation. -12glo + -84glo + 8glox = 84glo + -84glo + -28glox Combine like terms: -12glo + -84glo = -96glo -96glo + 8glox = 84glo + -84glo + -28glox Combine like terms: 84glo + -84glo = 0 -96glo + 8glox = 0 + -28glox -96glo + 8glox = -28glox Add '28glox' to each side of the equation. -96glo + 8glox + 28glox = -28glox + 28glox Combine like terms: 8glox + 28glox = 36glox -96glo + 36glox = -28glox + 28glox Combine like terms: -28glox + 28glox = 0 -96glo + 36glox = 0 Factor out the Greatest Common Factor (GCF), '12glo'. 12glo(-8 + 3x) = 0 Ignore the factor 12.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 '(-8 + 3x)' equal to zero and attempt to solve: Simplifying -8 + 3x = 0 Solving -8 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x = 0 + 8 3x = 0 + 8 Combine like terms: 0 + 8 = 8 3x = 8 Add '-3x' to each side of the equation. 3x + -3x = 8 + -3x Combine like terms: 3x + -3x = 0 0 = 8 + -3x Simplifying 0 = 8 + -3x 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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