Evaluate without using a calculator

Question

1) e^ln2 =x

2) ln(1/sqrt(e))=x

3)(1.45)^x=25

4)10=22(0.87)^q

Answer 1

1) e ^ ln 2 =x 

 

 ln ( e^ln2 ) = ln 2 = ln X

 

     X = 2

 

2 ) ln ( 1/ √e) = x 

 

      ln ( e^-1/2 ) = X

 

       -1/2 = X

 

3 ) ( 1.45) ^ x = 25

 

      X log 1.45 = log 25

  

      X = log 25/ log 1.45 

 

       X = 8.66 ( Calculator)

 

4 ) 

 

    10 = 22( 0.87) ^q

 

     q log 0.87) = log( 10/22) 

 

     q = log ( 10/22)/ log 0.87

 

     q = 5.66 ( Calculator)