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受欢迎的代数 >

log_{2x-5}(3x^2-7x-11)=2

解答

lo g_{2 x - 5} (3 x^{2} - 7 x - 11) = 2

解答

x = 4, x = 9

求解步骤

lo g_{2 x - 5} (3 x^{2} - 7 x - 11) = 2

使用对数运算法则

\frac{ln ( 3 x ^{2} - 7 x - 11 )}{ln ( 2 x - 5 )} = 2

在两边乘以

ln (2 x - 5)

\frac{ln ( 3 x ^{2} - 7 x - 11 )}{ln ( 2 x - 5 )} ln (2 x - 5) = 2 ln (2 x - 5)

化简

ln (3 x^{2} - 7 x - 11) = 2 ln (2 x - 5)

使用对数运算法则

3 x^{2} - 7 x - 11 = (2 x - 5)^{2}

解

3 x^{2} - 7 x - 11 = (2 x - 5)^{2} : x = 4, x = 9

x = 4, x = 9

验证解:

x = 4

真

, x = 9

真

解为

x = 4, x = 9

作图

流行的例子

ln(x^{0.5})=(ln(x))^{0.5}

ln (x^{0.5}) = (ln (x))^{0.5}

ln (7 x + e) = 9

2.85=-log_{10}(x)

2.85 = - lo g_{10} (x)

log_{2}((2x)/(4x-2))=1

lo g_{2} (\frac{2 x}{4 x - 2}) = 1

4log_{x}(2)-log_{2}(x)=3

4 lo g_{x} (2) - lo g_{2} (x) = 3