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受欢迎的代数 >

3^t-4t-1<0

解答

3^{t} - 4 t - 1 < 0

解答

t < - \frac{W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4} or t > - \frac{W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4}

+2

间隔符号

- \infty, - \frac{W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4} \cup - \frac{W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4}, \infty

十进制

t < 0 or t > 2

求解步骤

3^{t} - 4 t - 1 < 0

将

4 t

到右边

3^{t} - 1 < 4 t

将

1

到右边

3^{t} < 4 t + 1

将

3^{t} < 4 t + 1

调整为朗伯形式:

1 < (4 t + 1) e^{- l n (3) t}

用

(- t - \frac{1}{4}) ln (3) = u

和

t = - \frac{4 u + ln ( 3 )}{4 ln ( 3 )}

改写方程式

1 < (4 (- \frac{4 u + ln ( 3 )}{4 ln ( 3 )}) + 1) e^{- l n (3) (- \frac{4 u + l n ( 3 )}{4 l n ( 3 )})}

化简

1 < e^{\frac{4 u + l n ( 3 )}{4}} (- \frac{4 u + ln ( 3 )}{ln ( 3 )} + 1)

改写

1 < e^{\frac{4 u + l n ( 3 )}{4}} (- \frac{4 u + ln ( 3 )}{ln ( 3 )} + 1)

为朗伯形式:

\frac{e ^{\frac{4 u + l n ( 3 )}{4}} u}{e ^{\frac{l n ( 3 )}{4}}} > - \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}}

解

\frac{e ^{\frac{4 u + l n ( 3 )}{4}} u}{e ^{\frac{l n ( 3 )}{4}}} > - \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} : u < W_{- 1} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}}) or u > W_{0} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}})

u < W_{- 1} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}}) or u > W_{0} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}})

代回

(- t - \frac{1}{4}) ln (3) = u

，求解

t

解

(- t - \frac{1}{4}) ln (3) < W_{- 1} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}}) or (- t - \frac{1}{4}) ln (3) > W_{0} (- \frac{ln ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}}) : t < - \frac{W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4} or t > - \frac{W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4}

t < - \frac{W _{0} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4} or t > - \frac{W _{- 1} ( - \frac{l n ( 3 )}{4 e ^{\frac{l n ( 3 )}{4}}} )}{ln ( 3 )} - \frac{1}{4}

作图

流行的例子

3^{1/((x+1))}>9

3^{\frac{1}{( x + 1 )}} > 9

2^{x} + x - 3 < 0

2^{x} > - x + 3

(2^n)/((2^{n+2)-3)}< 1/4

\frac{2 ^{n}}{( 2 ^{n + 2} - 3 )} < \frac{1}{4}

((4^x+2))/9 <2^{x-1}

\frac{( 4 ^{x} + 2 )}{9} < 2^{x - 1}