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受欢迎的代数 >

3log_{8}(x)-log_{x}(64+1)=0

解答

3 lo g_{8} (x) - lo g_{x} (64 + 1) = 0

解答

x = 8^{\frac{l o g _{8} ( 65 )}{3}}, x = \frac{1}{8 ^{\frac{l o g _{8} ( 65 )}{3}}}

+1

十进制

x = 5.47952 \dots, x = 0.18249 \dots

求解步骤

3 lo g_{8} (x) - lo g_{x} (64 + 1) = 0

使用对数运算法则

3 lo g_{8} (x) - \frac{lo g _{8} ( 65 )}{lo g _{8} ( x )} = 0

用

lo g_{8} (x) = u

改写方程式

3 u - \frac{lo g _{8} ( 65 )}{u} = 0

解

3 u - \frac{lo g _{8} ( 65 )}{u} = 0 : u = \frac{lo g _{8} ( 65 )}{3}, u = - \frac{lo g _{8} ( 65 )}{3}

u = \frac{lo g _{8} ( 65 )}{3}, u = - \frac{lo g _{8} ( 65 )}{3}

代回

u = lo g_{8} (x)

，求解

x

解

lo g_{8} (x) = \frac{lo g _{8} ( 65 )}{3} : x = 8^{\frac{l o g _{8} ( 65 )}{3}}

解

lo g_{8} (x) = - \frac{lo g _{8} ( 65 )}{3} : x = \frac{1}{8 ^{\frac{l o g _{8} ( 65 )}{3}}}

x = 8^{\frac{l o g _{8} ( 65 )}{3}}, x = \frac{1}{8 ^{\frac{l o g _{8} ( 65 )}{3}}}

验证解:

x = 8^{\frac{l o g _{8} ( 65 )}{3}}

真

, x = \frac{1}{8 ^{\frac{l o g _{8} ( 65 )}{3}}}

真

解为

x = 8^{\frac{l o g _{8} ( 65 )}{3}}, x = \frac{1}{8 ^{\frac{l o g _{8} ( 65 )}{3}}}

作图

流行的例子

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

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

log_{y}(125)=-3/2

lo g_{y} (125) = - \frac{3}{2}

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

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

7 - 2 ln (x) = 2

solvefor H,p=-log_{10}(H)

so l v e f or H, p = - lo g_{10} (H)