sqrt e^9t =e^t

Question

could some one help me with this pre-calc question please ? Logarithms and their properties

Answer 1

Assuming this:

 

sqrt (e^9t) =e^t

 

(e^9t)^(1/2) =e^t

 

e^(9t/2) =e^t

 

9t/2 = t

 

9t/2 - t = 0

 

7t/2 = 0

 

t = 0

Answer 2

√e^9t = e ^t

 

e^(9/2)t  = e^t

 

  The = should not be there , because it is only true for t =0

 

  ln ( e^ (9t/2)  = 9t/2

 

   ln e ^t = t

 

     Maybe this was

 

    √e ^ 9t = e ^3

 

      e ^ (9t/2) = e ^3

 

         9t/2 = 3

 

           t = 6/9 = 2/3