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Simplifying log(4)(5x + 6) = log(4)(2x + -3) Reorder the terms: glo * 4(6 + 5x) = log(4)(2x + -3) Reorder the terms for easier multiplication: 4glo(6 + 5x) = log(4)(2x + -3) (6 * 4glo + 5x * 4glo) = log(4)(2x + -3) (24glo + 20glox) = log(4)(2x + -3) Reorder the terms: 24glo + 20glox = glo * 4(-3 + 2x) Reorder the terms for easier multiplication: 24glo + 20glox = 4glo(-3 + 2x) 24glo + 20glox = (-3 * 4glo + 2x * 4glo) 24glo + 20glox = (-12glo + 8glox) Solving 24glo + 20glox = -12glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glo' to each side of the equation. 24glo + 12glo + 20glox = -12glo + 12glo + 8glox Combine like terms: 24glo + 12glo = 36glo 36glo + 20glox = -12glo + 12glo + 8glox Combine like terms: -12glo + 12glo = 0 36glo + 20glox = 0 + 8glox 36glo + 20glox = 8glox Add '-8glox' to each side of the equation. 36glo + 20glox + -8glox = 8glox + -8glox Combine like terms: 20glox + -8glox = 12glox 36glo + 12glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 36glo + 12glox = 0 Factor out the Greatest Common Factor (GCF), '12glo'. 12glo(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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