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Simplifying Ln(5x) + -0.2x + -1 = 0 Remove parenthesis around (5x) nL * 5x + -0.2x + -1 = 0 Reorder the terms for easier multiplication: 5nL * x + -0.2x + -1 = 0 Multiply nL * x 5nxL + -0.2x + -1 = 0 Reorder the terms: -1 + 5nxL + -0.2x = 0 Solving -1 + 5nxL + -0.2x = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 5nxL + 1 + -0.2x = 0 + 1 Reorder the terms: -1 + 1 + 5nxL + -0.2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5nxL + -0.2x = 0 + 1 5nxL + -0.2x = 0 + 1 Combine like terms: 0 + 1 = 1 5nxL + -0.2x = 1 Add '0.2x' to each side of the equation. 5nxL + -0.2x + 0.2x = 1 + 0.2x Combine like terms: -0.2x + 0.2x = 0.0 5nxL + 0.0 = 1 + 0.2x 5nxL = 1 + 0.2x Divide each side by '5xL'. n = 0.2x-1L-1 + 0.04L-1 Simplifying n = 0.2x-1L-1 + 0.04L-1 Reorder the terms: n = 0.04L-1 + 0.2x-1L-1
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