1) log151 = 0

 
    Solution: 150 = 1
    That is, any number or expression raised to the power of 0 is defined
    as being equal to 1.

 2) log55 = 1
 
    Solution: 51 = 5
    That is, any expression/number raised to the power of one is the
    expression/number itself (unchanged).

 3) log33x = x

    Solution:  3x = 3x

 4) eln4 = 4
   
    Solution: Recall that if you do something to one side of an equation, you
    must do the same thing to the other side, in order for the equation to 
    remain the same.
    Step 1: take the ln of both side:  ln(eln4) = ln(4)
    Refer to property #7: ln(4)[ln(e)] = ln(4)
    ln(e) = 1 by definition: ln(4) = ln(4)  
    We get the same expression on both sides so the original equation is true.



 5) log107 + log104 = log1028 
 
    Solution: Left hand side of the equation:
              i)   log107 = 0.845
              ii)  log104 = 0.602
              iii) 0.845 + 0.602 = 1.447
              Right hand side of the equation:
              iv)  log28 = 1.447 also
              Thus,  1.447 = 1.447 which we know is correct.

 6) ln2 - ln5 = ln(2/5)

    Solution:  Left hand side of equation:
               i)   ln2 = 0.693
               ii)  ln5 = 1.609
               iii) ln2 - ln5 = 0.693 - 1.609 = -0.916
               Right hand side of equation:
                iv) ln(2/5) = ln(0.4) = -0.916
               Thus, -0.916 = -0.916 which we know to be correct.

 7) log1023 = 3log102

    Solution: log10(8) = 0.903 while  3log102 = 3(0.301)
                                             = 0.903
              Thus, both sides of the equation equal the same number which
              means the original statement must be true.