Find the inverse function if: 9 x = 2 e x 2

Question

Find the inverse function if:      9    x    =  2      e                  x        2

umgangistbf · Accepted Answer

9    x    =  2      e                  x        2              9  x  =  2      e                  x        2              ln  ⁡  (  9  x  )  =  ln  ⁡  (  2      e                  x        2              )  x  (  ln  ⁡  (  9  )  )  =  ln  ⁡  (  2  )  +  ln  ⁡  (      e                  x        2              )  x  (  ln  ⁡  (  9  )  )  =  ln  ⁡  (  2  )  +      x          2            x          2        −  ln  ⁡  (  9  )  x  +  ln  ⁡  (  2  )  =  0now solve using quadratic formula you get  x  =            ln      ⁡      (      9      )      +              [        (        ln        ⁡        9                  )                      2                          −        4        (        1        )        (        ln        ⁡        (        2        )        )        ]              2

Find the inverse function if: 9^x =2e^(x^2)

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