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Simplifying log(e)(3x + 7) = log(e)(x + -1) Reorder the terms: glo * e(7 + 3x) = log(e)(x + -1) Multiply glo * e eglo(7 + 3x) = log(e)(x + -1) (7 * eglo + 3x * eglo) = log(e)(x + -1) (7eglo + 3eglox) = log(e)(x + -1) Reorder the terms: 7eglo + 3eglox = glo * e(-1 + x) Multiply glo * e 7eglo + 3eglox = eglo(-1 + x) 7eglo + 3eglox = (-1 * eglo + x * eglo) 7eglo + 3eglox = (-1eglo + eglox) Solving 7eglo + 3eglox = -1eglo + eglox Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add 'eglo' to each side of the equation. 7eglo + eglo + 3eglox = -1eglo + eglo + eglox Combine like terms: 7eglo + eglo = 8eglo 8eglo + 3eglox = -1eglo + eglo + eglox Combine like terms: -1eglo + eglo = 0 8eglo + 3eglox = 0 + eglox 8eglo + 3eglox = eglox Add '-1eglox' to each side of the equation. 8eglo + 3eglox + -1eglox = eglox + -1eglox Combine like terms: 3eglox + -1eglox = 2eglox 8eglo + 2eglox = eglox + -1eglox Combine like terms: eglox + -1eglox = 0 8eglo + 2eglox = 0 Factor out the Greatest Common Factor (GCF), '2eglo'. 2eglo(4 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'eglo' equal to zero and attempt to solve: Simplifying eglo = 0 Solving eglo = 0 Move all terms containing e to the left, all other terms to the right. Simplifying eglo = 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing e to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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