log_{4}(3x)-1=log_{4-2+9}(x)

解答

lo g_{4} (3 x) - 1 = lo g_{4 - 2 + 9} (x)

x = 1 1^{\frac{2 l o g _{11} ( 2 ) - l o g _{11} ( 3 )}{1 - 2 l o g _{11} ( 2 )}}

十进制

x = 1.97767 \dots

求解步骤

lo g_{4} (3 x) - 1 = lo g_{4 - 2 + 9} (x)

使用对数运算法则

x = 1 1^{\frac{2 l o g _{11} ( 2 ) - l o g _{11} ( 3 )}{1 - 2 l o g _{11} ( 2 )}}

验证解:

x = 1 1^{\frac{2 l o g _{11} ( 2 ) - l o g _{11} ( 3 )}{1 - 2 l o g _{11} ( 2 )}}

真

解是

x = 1 1^{\frac{2 l o g _{11} ( 2 ) - l o g _{11} ( 3 )}{1 - 2 l o g _{11} ( 2 )}}

- \frac{ln ( x ) - 1}{x ^{2}} = 0

ln (x) = - 2 (0)^{2}

lo g_{8} (\frac{x - 2}{3}) = 1

so l v e f or x, 6.91 = - lo g_{10} (x)

ln (3) + ln (2 x^{2} + 4) = ln (12)