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Simplifying log[4](5x + -4) = log[4](3x + 8) Reorder the terms: glo * 4(-4 + 5x) = log[4](3x + 8) Reorder the terms for easier multiplication: 4glo(-4 + 5x) = log[4](3x + 8) (-4 * 4glo + 5x * 4glo) = log[4](3x + 8) (-16glo + 20glox) = log[4](3x + 8) Reorder the terms: -16glo + 20glox = glo * 4(8 + 3x) Reorder the terms for easier multiplication: -16glo + 20glox = 4glo(8 + 3x) -16glo + 20glox = (8 * 4glo + 3x * 4glo) -16glo + 20glox = (32glo + 12glox) Solving -16glo + 20glox = 32glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-32glo' to each side of the equation. -16glo + -32glo + 20glox = 32glo + -32glo + 12glox Combine like terms: -16glo + -32glo = -48glo -48glo + 20glox = 32glo + -32glo + 12glox Combine like terms: 32glo + -32glo = 0 -48glo + 20glox = 0 + 12glox -48glo + 20glox = 12glox Add '-12glox' to each side of the equation. -48glo + 20glox + -12glox = 12glox + -12glox Combine like terms: 20glox + -12glox = 8glox -48glo + 8glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -48glo + 8glox = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(-6 + x) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -1x 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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