The third term in the expansion of (1x+xlog10x)5 is 1, then x=

5C2(1x)5−2(xlog10x)2=1 5×42×1×1x3.x2(log10x)2=1 10×1x(log10x)2=1 1x(log10x)2=110 ∴x=10

5C2(1x)5−2(xlog10x)2=1 5×42×1×1x3.x2(log10x)2=1 10×1x(log10x)2=1 1x(log10x)2=110 ∴x=10

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The third term in the expansion of ${(\frac{1}{x} + x \log_{10} x)}^{5}$ is 1, then $x =$

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10^{3}

10^{2}

answer is B.

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^{5} C_{2} {(\frac{1}{x})}^{5 - 2} {(x \log_{10} x)}^{2} = 1

$\frac{5 \times 4}{2 \times 1} \times \frac{1}{x^{3}} . x^{2} {(\log_{10} x)}^{2} = 1$

$10 \times \frac{1}{x} {(\log_{10} x)}^{2} = 1$

$\frac{1}{x} {(\log_{10} x)}^{2} = \frac{1}{10}$

$∴ x = 10$

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