Changing an exponential function to logarithmicI have a question stating that P = 75 e − 0.005 t and they want to get t by itself.I used the example y = 2 x = x = l o g 2 ( y )To find that − 0.005 t = 75 l n ( P )So t = 75 l n ( P ) − 0.005 However apparently this isn't correct. Can someone please show me where I went wrong (not so much another way of doing it, but what was wrong in the working I used)Thanks

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Changing an exponential function to logarithmicI have a question stating that    P  =  75      e          −      0.005      t       and they want to get t by itself.I used the example   y  =      2    x    =  x  =  l  o      g    2    (  y  )To find that    −  0.005  t  =  75  l  n  (  P  )So   t  =            75      l      n      (      P      )              −      0.005      However apparently this isn&#039;t correct. Can someone please show me where I went wrong (not so much another way of doing it, but what was wrong in the working I used)Thanks

Marlee Guerra · Accepted Answer

P        =        75                  e                      −            0.005            t                                                      ⟺                                      P            75                          =                  e                      −            0.005            t                                                                                  ⟺                ln        ⁡                  (                      P            75                    )                =        ln        ⁡                  (                      e                          −              0.005              t                                )                                                                        ⟺                ln        ⁡                  (                      P            75                    )                =        −        0.005        t                                                                ⟺                t        =        −                  (                                    ln              ⁡              P              −              ln              ⁡              (              75              )                        0.005                    )

lobht98 · Accepted Answer

P=75exp(-0.005t) ===&amp;gt; ln(P) = ln(75) + ln(exp(-0.005t)) ===&amp;gt; ln(P) = ln(75) - 0.005t ===&amp;gt; t= (ln(P) - ln(75))/-0.005

Changing an exponential function to logarithmic I have a question stating that P = 75

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