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Simplifying log[2](3x + -7) = log[2](5x + 11) Reorder the terms: glo * 2(-7 + 3x) = log[2](5x + 11) Reorder the terms for easier multiplication: 2glo(-7 + 3x) = log[2](5x + 11) (-7 * 2glo + 3x * 2glo) = log[2](5x + 11) (-14glo + 6glox) = log[2](5x + 11) Reorder the terms: -14glo + 6glox = glo * 2(11 + 5x) Reorder the terms for easier multiplication: -14glo + 6glox = 2glo(11 + 5x) -14glo + 6glox = (11 * 2glo + 5x * 2glo) -14glo + 6glox = (22glo + 10glox) Solving -14glo + 6glox = 22glo + 10glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-22glo' to each side of the equation. -14glo + -22glo + 6glox = 22glo + -22glo + 10glox Combine like terms: -14glo + -22glo = -36glo -36glo + 6glox = 22glo + -22glo + 10glox Combine like terms: 22glo + -22glo = 0 -36glo + 6glox = 0 + 10glox -36glo + 6glox = 10glox Add '-10glox' to each side of the equation. -36glo + 6glox + -10glox = 10glox + -10glox Combine like terms: 6glox + -10glox = -4glox -36glo + -4glox = 10glox + -10glox Combine like terms: 10glox + -10glox = 0 -36glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-4glo'. -4glo(9 + x) = 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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