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受欢迎的代数 >

(log_{10}(6-x^2))/(log_{10)(3x-4)}=2

解答

\frac{lo g _{10} ( 6 - x ^{2} )}{lo g _{10} ( 3 x - 4 )} = 2

解答

x = \frac{6 + 11}{5}

+1

十进制

x = 1.86332 \dots

求解步骤

\frac{lo g _{10} ( 6 - x ^{2} )}{lo g _{10} ( 3 x - 4 )} = 2

在两边乘以

lo g_{10} (3 x - 4)

\frac{lo g _{10} ( 6 - x ^{2} )}{lo g _{10} ( 3 x - 4 )} lo g_{10} (3 x - 4) = 2 lo g_{10} (3 x - 4)

化简

lo g_{10} (6 - x^{2}) = 2 lo g_{10} (3 x - 4)

使用对数运算法则

6 - x^{2} = (3 x - 4)^{2}

解

6 - x^{2} = (3 x - 4)^{2} : x = \frac{6 + 11}{5}, x = \frac{6 - 11}{5}

x = \frac{6 + 11}{5}, x = \frac{6 - 11}{5}

验证解:

x = \frac{6 + 11}{5}

真

, x = \frac{6 - 11}{5}

假

解是

x = \frac{6 + 11}{5}

作图

流行的例子

log_{4}(x+12)-log_{4}(5-x)=2

lo g_{4} (x + 12) - lo g_{4} (5 - x) = 2

lo g_{2} (x + 7) = 5

log_{b}(3)= 1/2

lo g_{b} (3) = \frac{1}{2}

ln ((2 x + 3)^{3}) = 1

(log_{10}(2x^2+1))/(log_{10)(x+1)}=2

\frac{lo g _{10} ( 2 x ^{2} + 1 )}{lo g _{10} ( x + 1 )} = 2