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受欢迎的代数 >

log_{10}(x^5)=(log_{10}(x^5))^3

解答

lo g_{10} (x^{5}) = (lo g_{10} (x^{5}))^{3}

解答

x = 1, x = \frac{1}{5 10}, x = 510

+1

十进制

x = 1, x = 0.63095 \dots, x = 1.58489 \dots

求解步骤

lo g_{10} (x^{5}) = (lo g_{10} (x^{5}))^{3}

用

lo g_{10} (x^{5}) = u

改写方程式

u = (u)^{3}

解

u = u^{3} : u = 0, u = - 1, u = 1

u = 0, u = - 1, u = 1

代回

u = lo g_{10} (x^{5})

，求解

x

解

lo g_{10} (x^{5}) = 0 : x = 1

解

lo g_{10} (x^{5}) = - 1 : x = \frac{1}{5 10}

解

lo g_{10} (x^{5}) = 1 : x = 510

x = 1, x = \frac{1}{5 10}, x = 510

验证解:

x = 1

真

, x = \frac{1}{5 10}

真

, x = 510

真

解为

x = 1, x = \frac{1}{5 10}, x = 510

作图

流行的例子

log_{10}(-2x)+log_{10}(6)=1

lo g_{10} (- 2 x) + lo g_{10} (6) = 1

log_{x}(512)= 3/2

lo g_{x} (512) = \frac{3}{2}

ln(4)-ln(3)=2ln(x)-ln(x+1)

ln (4) - ln (3) = 2 ln (x) - ln (x + 1)

log_{8}(4x+4)=2

lo g_{8} (4 x + 4) = 2

12x^2ln(x)+7x^2=0

12 x^{2} ln (x) + 7 x^{2} = 0