Solve the following equations: 3 x = 8 , e 2 x − 2 e x − 5 = 0 , ln ⁡ ( 4 x + 1 ) = 20

Question

Solve the following equations:       3          x        =  8  ,      e          2      x        −  2      e          x        −  5  =  0  ,  ln  ⁡  (  4  x  +  1  )  =  20

Izabelle Frost · Accepted Answer

3          x        =  8  ln  ⁡      3          x        =  ln  ⁡  8  x  ln  ⁡  3  =  ln  ⁡  8  x  =  ln  ⁡  8      /    ln  ⁡  3.      e          2      x        −  2      e          x        −  5  =  0Let   y  =      e          x      .      y          2        −  2  y  −  5  =  0  y  =  (  2  ±  (  4  +  20  )  1      /    2  )      /    2  =  1  ±      6          1              /            2      .      e          x        =  1  ±      6          1              /            2      .  x  =      {    ln    ⁡          |        1    +          6              1                  /                2                    |        ,    ln    ⁡          |        1    −          6              1                  /                2                    |        }    ln  ⁡  (  4  x  +  1  )  =  20  4  x  +  1  =      e          20      .  4  x  =      e          20        −  1  x  =  (      e          20        −  1  )      /    4

Solve the following equations: 3^x = 8, e^(2x) -2e^x - 5 = 0, ln(4x + 1) = 20

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