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受欢迎的代数 >

ln(x^2+2)-ln(x-1)=2

解答

ln (x^{2} + 2) - ln (x - 1) = 2

解答

x = \frac{e ^{2} + e ^{4} - 4 ( 2 + e ^{2} )}{2}, x = \frac{e ^{2} - e ^{4} - 4 ( 2 + e ^{2} )}{2}

+1

十进制

x = 5.75862 \dots, x = 1.63043 \dots

求解步骤

ln (x^{2} + 2) - ln (x - 1) = 2

两边加上

ln (x - 1)

ln (x^{2} + 2) - ln (x - 1) + ln (x - 1) = 2 + ln (x - 1)

化简

ln (x^{2} + 2) = 2 + ln (x - 1)

使用对数运算法则

x^{2} + 2 = e^{2} (x - 1)

解

x^{2} + 2 = e^{2} (x - 1) : x = \frac{e ^{2} + e ^{4} - 4 ( 2 + e ^{2} )}{2}, x = \frac{e ^{2} - e ^{4} - 4 ( 2 + e ^{2} )}{2}

x = \frac{e ^{2} + e ^{4} - 4 ( 2 + e ^{2} )}{2}, x = \frac{e ^{2} - e ^{4} - 4 ( 2 + e ^{2} )}{2}

验证解:

x = \frac{e ^{2} + e ^{4} - 4 ( 2 + e ^{2} )}{2}

真

, x = \frac{e ^{2} - e ^{4} - 4 ( 2 + e ^{2} )}{2}

真

解为

x = \frac{e ^{2} + e ^{4} - 4 ( 2 + e ^{2} )}{2}, x = \frac{e ^{2} - e ^{4} - 4 ( 2 + e ^{2} )}{2}

作图

流行的例子

15=6log_{4}(8x)

15 = 6 lo g_{4} (8 x)

ln(x)-3/(ln(x))=2

ln (x) - \frac{3}{ln ( x )} = 2

log_{3}(x+17)-2=log_{3}(2x)

lo g_{3} (x + 17) - 2 = lo g_{3} (2 x)

4=(ln(2x))/(ln(4x))

4 = \frac{ln ( 2 x )}{ln ( 4 x )}

2 lo g_{2} (x) = 4