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Simplifying Loge(x + -1a) + x = 1 Reorder the terms: egoL(-1a + x) + x = 1 (-1a * egoL + x * egoL) + x = 1 (-1aegoL + egoxL) + x = 1 Solving -1aegoL + egoxL + x = 1 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1egoxL' to each side of the equation. -1aegoL + egoxL + -1egoxL + x = 1 + -1egoxL Combine like terms: egoxL + -1egoxL = 0 -1aegoL + 0 + x = 1 + -1egoxL -1aegoL + x = 1 + -1egoxL Add '-1x' to each side of the equation. -1aegoL + x + -1x = 1 + -1egoxL + -1x Combine like terms: x + -1x = 0 -1aegoL + 0 = 1 + -1egoxL + -1x -1aegoL = 1 + -1egoxL + -1x Divide each side by '-1egoL'. a = -1e-1g-1o-1L-1 + x + e-1g-1o-1xL-1 Simplifying a = -1e-1g-1o-1L-1 + x + e-1g-1o-1xL-1 Reorder the terms: a = -1e-1g-1o-1L-1 + e-1g-1o-1xL-1 + x
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