f(x)=ln(sqrt(5x+1)(x^2+5))

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Solution for f(x)=ln(sqrt(5x+1)(x^2+5)) equation:


Simplifying
f(x) = ln(sqrt(5x + 1)(x2 + 5))

Multiply f * x
fx = ln(sqrt(5x + 1)(x2 + 5))

Reorder the terms:
fx = ln(qrst(1 + 5x)(x2 + 5))

Reorder the terms:
fx = ln(qrst(1 + 5x)(5 + x2))

Multiply (1 + 5x) * (5 + x2)
fx = ln(qrst(1(5 + x2) + 5x * (5 + x2)))
fx = ln(qrst((5 * 1 + x2 * 1) + 5x * (5 + x2)))
fx = ln(qrst((5 + 1x2) + 5x * (5 + x2)))
fx = ln(qrst(5 + 1x2 + (5 * 5x + x2 * 5x)))
fx = ln(qrst(5 + 1x2 + (25x + 5x3)))

Reorder the terms:
fx = ln(qrst(5 + 25x + 1x2 + 5x3))
fx = ln(qrst(5 + 25x + 1x2 + 5x3))
fx = ln((5 * qrst + 25x * qrst + 1x2 * qrst + 5x3 * qrst))
fx = ln((5qrst + 25qrstx + 1qrstx2 + 5qrstx3))
fx = (5qrst * ln + 25qrstx * ln + 1qrstx2 * ln + 5qrstx3 * ln)
fx = (5lnqrst + 25lnqrstx + 1lnqrstx2 + 5lnqrstx3)

Solving
fx = 5lnqrst + 25lnqrstx + 1lnqrstx2 + 5lnqrstx3

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = 5lnqrstx-1 + 25lnqrst + lnqrstx + 5lnqrstx2

Simplifying
f = 5lnqrstx-1 + 25lnqrst + lnqrstx + 5lnqrstx2

Reorder the terms:
f = 25lnqrst + 5lnqrstx-1 + lnqrstx + 5lnqrstx2

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