Question

ПОМОГИТЕ РЕШИТЬ 

    $<var>x ^3^l^g^x=10*x^2</var>$

Answer 1

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Answer 2

$x^{3lg x} = 10x^2\\ 10 = x^{log_{x} 10}\\ x^{3lg x} = x^{log_{x} 10}x^2\\ x^{3lg x} = x^{log_{x} 10 + 2}\\ 3lg x = log_{x}10 + 2 | * lg x, x > 0, x ne 1\\ 3lg^2 x = 1 + 2lg x\\ 3lg^2 x - 2lg x - 1 = 0, t = lg x$

$3t^2 - 2t - 1 = 0\\ 3t^2 - 3t + t - 1 = 0\\ 3t(t - 1) + 1(t - 1) = 0\\ (3t + 1)(t - 1) = 0\\ 1) 3t + 1 = 0, 3t = -1, t = -frac{1}{3}\\ lg x = -frac{1}{3}, boxed{x = frac{1}{sqrt[3]{10}} }\\ 2) t - 1 = 0, t = 1\\ lg x = 1, boxed{x = 10}$