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Simplifying f(x) = ln[(2x + 1) * 7(3x + 1) * 9] Multiply f * x fx = ln[(2x + 1) * 7(3x + 1) * 9] Reorder the terms: fx = ln[(1 + 2x) * 7(3x + 1) * 9] Reorder the terms: fx = ln[(1 + 2x) * 7(1 + 3x) * 9] Reorder the terms for easier multiplication: fx = ln[7 * 9(1 + 2x)(1 + 3x)] Multiply 7 * 9 fx = ln[63(1 + 2x)(1 + 3x)] Multiply (1 + 2x) * (1 + 3x) fx = ln[63(1(1 + 3x) + 2x * (1 + 3x))] fx = ln[63((1 * 1 + 3x * 1) + 2x * (1 + 3x))] fx = ln[63((1 + 3x) + 2x * (1 + 3x))] fx = ln[63(1 + 3x + (1 * 2x + 3x * 2x))] fx = ln[63(1 + 3x + (2x + 6x2))] Combine like terms: 3x + 2x = 5x fx = ln[63(1 + 5x + 6x2)] fx = ln[(1 * 63 + 5x * 63 + 6x2 * 63)] fx = ln[(63 + 315x + 378x2)] fx = [63 * ln + 315x * ln + 378x2 * ln] fx = [63ln + 315lnx + 378lnx2] Solving fx = 63ln + 315lnx + 378lnx2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 63lnx-1 + 315ln + 378lnx Simplifying f = 63lnx-1 + 315ln + 378lnx Reorder the terms: f = 315ln + 63lnx-1 + 378lnx
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