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Simplifying ln(x) + kn(7x) = -3 Multiply ln * x lnx + kn(7x) = -3 Remove parenthesis around (7x) lnx + kn * 7x = -3 Reorder the terms for easier multiplication: lnx + 7kn * x = -3 Multiply kn * x lnx + 7knx = -3 Reorder the terms: 7knx + lnx = -3 Solving 7knx + lnx = -3 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 7knx + lnx + -1lnx = -3 + -1lnx Combine like terms: lnx + -1lnx = 0 7knx + 0 = -3 + -1lnx 7knx = -3 + -1lnx Divide each side by '7nx'. k = -0.4285714286n-1x-1 + -0.1428571429l Simplifying k = -0.4285714286n-1x-1 + -0.1428571429l Reorder the terms: k = -0.1428571429l + -0.4285714286n-1x-1
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