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Общий знаменатель 5/((1-log(4)/log(6))*log( ... -(6*e^-(log(2)*x))/log(2)

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
                                         -log(2)*x
                 5                    6*E         
----------------------------------- - ------------
                     /    log(4)\        log(2)   
                     |1 - ------|*x               
/    log(4)\         \    log(6)/                 
|1 - ------|*log(6)*6                             
\    log(6)/
$$- \frac{6 e^{- x \log{\left (2 \right )}}}{\log{\left (2 \right )}} + \frac{5}{6^{x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)} \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right) \log{\left (6 \right )}}$$
Степени [src]
                        /    log(4)\
                     -x*|1 - ------|
     -x*log(2)          \    log(6)/
  6*e             5*6               
- ------------ + -------------------
     log(2)      /    log(4)\       
                 |1 - ------|*log(6)
                 \    log(6)/
$$- \frac{6 e^{- x \log{\left (2 \right )}}}{\log{\left (2 \right )}} + \frac{5 \cdot 6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)}}{\left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right) \log{\left (6 \right )}}$$
Численный ответ [src]
12.3315173118822*6.0^(-0.226294385530917*x) - 8.65617024533378*2.71828182845905^(-0.693147180559945*x)
Рациональный знаменатель [src]
    /    log(4)\ /       x*log(4)                  x*log(4)                                          \           
 -x*|1 - ------| |   x - --------              x - --------                                          |           
    \    log(6)/ |        log(6)     2              log(6)                     x*log(2)              |  -x*log(2)
6               *\6*6            *log (6) - 6*6            *log(4)*log(6) - 5*e        *log(2)*log(6)/*e         
-----------------------------------------------------------------------------------------------------------------
                                         (-log(6) + log(4))*log(2)*log(6)
$$\frac{6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)} e^{- x \log{\left (2 \right )}}}{\left(- \log{\left (6 \right )} + \log{\left (4 \right )}\right) \log{\left (2 \right )} \log{\left (6 \right )}} \left(- 6 \cdot 6^{- \frac{x \log{\left (4 \right )}}{\log{\left (6 \right )}} + x} \log{\left (4 \right )} \log{\left (6 \right )} + 6 \cdot 6^{- \frac{x \log{\left (4 \right )}}{\log{\left (6 \right )}} + x} \log^{2}{\left (6 \right )} - 5 e^{x \log{\left (2 \right )}} \log{\left (2 \right )} \log{\left (6 \right )}\right)$$
Объединение рациональных выражений [src]
/                        x*(-log(4) + log(6))      x*log(2)       \  -x*(-log(4) + log(6))  -x*log(2)
\- 6*(-log(4) + log(6))*e                     + 5*e        *log(2)/*e                     *e         
-----------------------------------------------------------------------------------------------------
                                      (-log(4) + log(6))*log(2)
$$\frac{e^{- x \left(- \log{\left (4 \right )} + \log{\left (6 \right )}\right)} e^{- x \log{\left (2 \right )}}}{\left(- \log{\left (4 \right )} + \log{\left (6 \right )}\right) \log{\left (2 \right )}} \left(- 6 \left(- \log{\left (4 \right )} + \log{\left (6 \right )}\right) e^{x \left(- \log{\left (4 \right )} + \log{\left (6 \right )}\right)} + 5 e^{x \log{\left (2 \right )}} \log{\left (2 \right )}\right)$$
Общее упрощение [src]
/ x*log(2)                                 x*(-log(2) + log(3))\  -x*log(3)
\e        *log(32) + 6*(-log(3) + log(2))*e                    /*e         
---------------------------------------------------------------------------
                         (-log(2) + log(3))*log(2)
$$\frac{e^{- x \log{\left (3 \right )}}}{\left(- \log{\left (2 \right )} + \log{\left (3 \right )}\right) \log{\left (2 \right )}} \left(6 \left(- \log{\left (3 \right )} + \log{\left (2 \right )}\right) e^{x \left(- \log{\left (2 \right )} + \log{\left (3 \right )}\right)} + e^{x \log{\left (2 \right )}} \log{\left (32 \right )}\right)$$
Собрать выражение [src]
        /    log(4)\                
     -x*|1 - ------|                
        \    log(6)/       -log(2)*x
    6                   6*E         
5*------------------- - ------------
  /    log(4)\             log(2)   
  |1 - ------|*log(6)               
  \    log(6)/
$$- \frac{6 e^{- x \log{\left (2 \right )}}}{\log{\left (2 \right )}} + 5 \frac{6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)}}{\left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right) \log{\left (6 \right )}}$$
 /                       x*(-log(2) + log(3))    x*log(2)        \  x*(-log(3) + log(2))  -x*log(2) 
-\(-log(729) + log(64))*e                     + e        *log(32)/*e                    *e          
----------------------------------------------------------------------------------------------------
                                     (-log(3) + log(2))*log(2)
$$- \frac{e^{x \left(- \log{\left (3 \right )} + \log{\left (2 \right )}\right)} e^{- x \log{\left (2 \right )}}}{\left(- \log{\left (3 \right )} + \log{\left (2 \right )}\right) \log{\left (2 \right )}} \left(\left(- \log{\left (729 \right )} + \log{\left (64 \right )}\right) e^{x \left(- \log{\left (2 \right )} + \log{\left (3 \right )}\right)} + e^{x \log{\left (2 \right )}} \log{\left (32 \right )}\right)$$
Общий знаменатель [src]
 /     x             3*x*log(2)              x       \ 
-\- 6*6 *log(6) + 5*e          *log(2) + 12*6 *log(2)/ 
-------------------------------------------------------
     x    2     x*log(2)    x  x*log(2)                
  2*6 *log (2)*e         - 6 *e        *log(2)*log(6)
$$- \frac{- 6 \cdot 6^{x} \log{\left (6 \right )} + 12 \cdot 6^{x} \log{\left (2 \right )} + 5 e^{3 x \log{\left (2 \right )}} \log{\left (2 \right )}}{- 6^{x} e^{x \log{\left (2 \right )}} \log{\left (2 \right )} \log{\left (6 \right )} + 2 \cdot 6^{x} e^{x \log{\left (2 \right )}} \log^{2}{\left (2 \right )}}$$
Комбинаторика [src]
     /    log(4)\                                                                                        
  -x*|1 - ------|                                                                                        
     \    log(6)/ /   x*log(2)             x  -2*x*log(2)              x  -2*x*log(2)       \  -x*log(2) 
-6               *\5*e        *log(2) - 6*6 *e           *log(6) + 12*6 *e           *log(2)/*e          
---------------------------------------------------------------------------------------------------------
                                       (-log(6) + 2*log(2))*log(2)
$$- \frac{6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)} e^{- x \log{\left (2 \right )}}}{\left(- \log{\left (6 \right )} + 2 \log{\left (2 \right )}\right) \log{\left (2 \right )}} \left(- 6 \cdot 6^{x} e^{- 2 x \log{\left (2 \right )}} \log{\left (6 \right )} + 12 \cdot 6^{x} e^{- 2 x \log{\left (2 \right )}} \log{\left (2 \right )} + 5 e^{x \log{\left (2 \right )}} \log{\left (2 \right )}\right)$$
Раскрыть выражение [src]
                        /    log(4)\
                     -x*|1 - ------|
     -log(2)*x          \    log(6)/
  6*E             5*6               
- ------------ + -------------------
     log(2)      /    log(4)\       
                 |1 - ------|*log(6)
                 \    log(6)/
$$- \frac{6 e^{- x \log{\left (2 \right )}}}{\log{\left (2 \right )}} + \frac{5 \cdot 6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)}}{\left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right) \log{\left (6 \right )}}$$
                        /    log(4)\
                     -x*|1 - ------|
     -x*log(2)          \    log(6)/
  6*e             5*6               
- ------------ + -------------------
     log(2)      /    log(4)\       
                 |1 - ------|*log(6)
                 \    log(6)/
$$- \frac{6 e^{- x \log{\left (2 \right )}}}{\log{\left (2 \right )}} + \frac{5 \cdot 6^{- x \left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right)}}{\left(- \frac{\log{\left (4 \right )}}{\log{\left (6 \right )}} + 1\right) \log{\left (6 \right )}}$$