how to write in logarithmic form

Question

how do I write these in logarithmic form?

 

 

1.  3^4 = 81

 

 

 

2.  (1/2)^4 = 1/16

 

 

 

solve for x

 

1.  log_x32 = 5

 

 

2.  log₂64 = x

 

 

thankyou

 

 

 

 

Answer 1

The rule to remember for going from exponent to logarithm is to remember that the base of the logarithm, is the base of the exponent (and vice versa).  The other two numbers swap to other sides of the equals

 

So 3^4 = 81 becomes   log₃ 81 = 4.

 

Also log₂64 = X   becomes 2^X = 64.    So X=6.