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受欢迎的代数 >

log_{10}((x^2)/(x-1))=3

解答

lo g_{10} (\frac{x ^{2}}{x - 1}) = 3

解答

x = 10 (50 + 2490), x = 10 (50 - 2490)

+1

十进制

x = 998.99899 \dots, x = 1.00100 \dots

求解步骤

lo g_{10} (\frac{x ^{2}}{x - 1}) = 3

使用对数运算法则

\frac{x ^{2}}{x - 1} = 1 0^{3}

在两边乘以

x - 1

\frac{x ^{2}}{x - 1} (x - 1) = 1 0^{3} (x - 1)

化简

x^{2} = 1000 (x - 1)

解

x^{2} = 1000 (x - 1) : x = 10 (50 + 2490), x = 10 (50 - 2490)

x = 10 (50 + 2490), x = 10 (50 - 2490)

验证解:

x = 10 (50 + 2490)

真

, x = 10 (50 - 2490)

真

解为

x = 10 (50 + 2490), x = 10 (50 - 2490)

作图

流行的例子

(x + y i)^{2} = 3 - 4 i

\frac{z - i}{z} = 2 + i

(x - y i)^{2} = - 8 - 6 i

z^{2} = i

z^{2} = 3 - 4 i