Question

questões exponenciais alguem me ajuda a resolver ;s

 

8x .4x . 2 = 16 . 2² . 32 

 

9x . 3²x = 27 . 81x . 27² 

 

49x : 7² = 49²  . 7 

 

100²x : 10000 = 1000² 

Answer 1

8x .4x . 2 = 16 . 2² . 32 
 2^3^x .2^2^x .2 = 2^4.2^2.2^5
        2.^5x = 2^11. 2^-1
           2^5x = 2^10
                 5x = 10
                   x = 2

9x . 3²x = 27 . 81x . 27²  
 (3^2)^x. (3^2)^x = (3^4)^x.3^3.(3^3)^2
         3^4x = 3^4x . 3^9
         3^4x  = 3^9
         3^4x
          3^(4x-4x) = 3^9
                  0x = 9
          

49x : 7² = 49²  . 7  
     7^2x  = (7^2)^2.7
       7^2
      7^2x = 7^2.7^4.7
        7^2x = 7^7
              2x = 7 ==> x = 7/2

100²x : 10000 = 1000² 
    (10^2)^x   = (10^3)^2
      10^4
      10^2x = 10^6.10^4
       10^2x = 10^10
              2x = 10
                x = 5

Answer 2

8x * 4x * 2=16 * 2² * 32
32x * 2 = 2048 (apenas multipliquei todos)
x² = 2048/ 64 
x= sqrt32
x= 5,6

9x * 3²x = 27 * 81x *27²
9x *9x = 27*81x*729
81x²/81x = 27 * 729
x = 19683


49x/7²= 49²*7
49x/49= 2401*7
x = 16807


100²x/10000=1000²
10000x/10000= 1000000
x = 1000000