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Simplifying loge(x + 1) + loge(x + -3) = loge(10) Reorder the terms: eglo(1 + x) + loge(x + -3) = loge(10) (1 * eglo + x * eglo) + loge(x + -3) = loge(10) (1eglo + eglox) + loge(x + -3) = loge(10) Reorder the terms: 1eglo + eglox + eglo(-3 + x) = loge(10) 1eglo + eglox + (-3 * eglo + x * eglo) = loge(10) 1eglo + eglox + (-3eglo + eglox) = loge(10) Reorder the terms: 1eglo + -3eglo + eglox + eglox = loge(10) Combine like terms: 1eglo + -3eglo = -2eglo -2eglo + eglox + eglox = loge(10) Combine like terms: eglox + eglox = 2eglox -2eglo + 2eglox = loge(10) Reorder the terms for easier multiplication: -2eglo + 2eglox = 10eglo Solving -2eglo + 2eglox = 10eglo Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-10eglo' to each side of the equation. -2eglo + -10eglo + 2eglox = 10eglo + -10eglo Combine like terms: -2eglo + -10eglo = -12eglo -12eglo + 2eglox = 10eglo + -10eglo Combine like terms: 10eglo + -10eglo = 0 -12eglo + 2eglox = 0 Factor out the Greatest Common Factor (GCF), '2eglo'. 2eglo(-6 + 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing e to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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