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Simplifying log3(14x + -3) = log3(6x + 5) Reorder the terms: g3lo(-3 + 14x) = log3(6x + 5) (-3 * g3lo + 14x * g3lo) = log3(6x + 5) (-3g3lo + 14g3lox) = log3(6x + 5) Reorder the terms: -3g3lo + 14g3lox = g3lo(5 + 6x) -3g3lo + 14g3lox = (5 * g3lo + 6x * g3lo) -3g3lo + 14g3lox = (5g3lo + 6g3lox) Solving -3g3lo + 14g3lox = 5g3lo + 6g3lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5g3lo' to each side of the equation. -3g3lo + -5g3lo + 14g3lox = 5g3lo + -5g3lo + 6g3lox Combine like terms: -3g3lo + -5g3lo = -8g3lo -8g3lo + 14g3lox = 5g3lo + -5g3lo + 6g3lox Combine like terms: 5g3lo + -5g3lo = 0 -8g3lo + 14g3lox = 0 + 6g3lox -8g3lo + 14g3lox = 6g3lox Add '-6g3lox' to each side of the equation. -8g3lo + 14g3lox + -6g3lox = 6g3lox + -6g3lox Combine like terms: 14g3lox + -6g3lox = 8g3lox -8g3lo + 8g3lox = 6g3lox + -6g3lox Combine like terms: 6g3lox + -6g3lox = 0 -8g3lo + 8g3lox = 0 Factor out the Greatest Common Factor (GCF), '8g3lo'. 8g3lo(-1 + x) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'g3lo' equal to zero and attempt to solve: Simplifying g3lo = 0 Solving g3lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g3lo = 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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