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受欢迎的代数 >

16ln(x)= 1/(ln(x))

解答

16 ln (x) = \frac{1}{ln ( x )}

解答

x = 4 e, x = \frac{1}{4 e}

+1

十进制

x = 1.28402 \dots, x = 0.77880 \dots

求解步骤

16 ln (x) = \frac{1}{ln ( x )}

在两边乘以

ln (x)

16 ln (x) ln (x) = \frac{1}{ln ( x )} ln (x)

化简

16 ln (x) ln (x) : 16 ln^{2} (x)

16 ln^{2} (x) = 1

用

ln (x) = u

改写方程式

16 u^{2} = 1

解

16 u^{2} = 1 : u = \frac{1}{16}, u = - \frac{1}{16}

u = \frac{1}{16}, u = - \frac{1}{16}

代回

u = ln (x)

，求解

x

解

ln (x) = \frac{1}{16} : x = 4 e

解

ln (x) = - \frac{1}{16} : x = \frac{1}{4 e}

x = 4 e, x = \frac{1}{4 e}

验证解:

x = 4 e

真

, x = \frac{1}{4 e}

真

解为

x = 4 e, x = \frac{1}{4 e}

作图

流行的例子

log_{3}(-2x-10)=2+log_{3}(6)

lo g_{3} (- 2 x - 10) = 2 + lo g_{3} (6)

solvefor x,ln(2x+1)=2-ln(x)

so l v e f or x, ln (2 x + 1) = 2 - ln (x)

log_{10}(x-2)=1.258

lo g_{10} (x - 2) = 1.258

log_{7}(10x)+20=0

lo g_{7} (10 x) + 20 = 0

lo g_{3} (x) = 2.2