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Simplifying log[4](2x + -7) = log[4](3x + -13) Reorder the terms: glo * 4(-7 + 2x) = log[4](3x + -13) Reorder the terms for easier multiplication: 4glo(-7 + 2x) = log[4](3x + -13) (-7 * 4glo + 2x * 4glo) = log[4](3x + -13) (-28glo + 8glox) = log[4](3x + -13) Reorder the terms: -28glo + 8glox = glo * 4(-13 + 3x) Reorder the terms for easier multiplication: -28glo + 8glox = 4glo(-13 + 3x) -28glo + 8glox = (-13 * 4glo + 3x * 4glo) -28glo + 8glox = (-52glo + 12glox) Solving -28glo + 8glox = -52glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '52glo' to each side of the equation. -28glo + 52glo + 8glox = -52glo + 52glo + 12glox Combine like terms: -28glo + 52glo = 24glo 24glo + 8glox = -52glo + 52glo + 12glox Combine like terms: -52glo + 52glo = 0 24glo + 8glox = 0 + 12glox 24glo + 8glox = 12glox Add '-12glox' to each side of the equation. 24glo + 8glox + -12glox = 12glox + -12glox Combine like terms: 8glox + -12glox = -4glox 24glo + -4glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 24glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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