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Simplifying log19(x2 + 17) = log19(8x + 2) Reorder the terms: g19lo(17 + x2) = log19(8x + 2) (17 * g19lo + x2 * g19lo) = log19(8x + 2) (17g19lo + g19lox2) = log19(8x + 2) Reorder the terms: 17g19lo + g19lox2 = g19lo(2 + 8x) 17g19lo + g19lox2 = (2 * g19lo + 8x * g19lo) 17g19lo + g19lox2 = (2g19lo + 8g19lox) Solving 17g19lo + g19lox2 = 2g19lo + 8g19lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2g19lo' to each side of the equation. 17g19lo + -2g19lo + g19lox2 = 2g19lo + -2g19lo + 8g19lox Combine like terms: 17g19lo + -2g19lo = 15g19lo 15g19lo + g19lox2 = 2g19lo + -2g19lo + 8g19lox Combine like terms: 2g19lo + -2g19lo = 0 15g19lo + g19lox2 = 0 + 8g19lox 15g19lo + g19lox2 = 8g19lox Add '-8g19lox' to each side of the equation. 15g19lo + -8g19lox + g19lox2 = 8g19lox + -8g19lox Combine like terms: 8g19lox + -8g19lox = 0 15g19lo + -8g19lox + g19lox2 = 0 Factor out the Greatest Common Factor (GCF), 'g19lo'. g19lo(15 + -8x + x2) = 0 Factor a trinomial. g19lo((3 + -1x)(5 + -1x)) = 0Subproblem 1
Set the factor 'g19lo' equal to zero and attempt to solve: Simplifying g19lo = 0 Solving g19lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g19lo = 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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