Natural Logarithms

Hi everyone
       kiran is hear,
  on friday we learned Natural Logarithms.
 Common logarithms : y = logx-> 10^y = x
                                  x = logy -> 10^x = y

Natural logarithms:y= in x -> e^y = x
                             x = in y ->e^x = y

all natural logarithms use the same laws and patterns as common logarithms.
   Division - subtraction
   Multiplication - Addition
   Exponents - Move to the front
   Same base - Cancel
   Change of Base - use e instead of 10
 
  Example 1 :
                    Evaluate to 3 decimal places.
          1)  e^4.2
              66.686
           
          2) In (7.6943)
                2.040

  Example 2 :
                  Evaluate without using the calculator :

          (3 In e) .(Ιν ε^5)

          = (3.1).(-4.5)

             3.(-20)

              -60

Example 3 :

               slove for x

   1) in e^3x = 14

          3x =14

          x = 14/3

   2) e^3x+5 =100

    ine^3x+5 = le 100

    3x =ln_e100-5

                                      Ine 100-5

               

      _{X  =  -------------------}

                     3               x= 0.1316ans.