Since there is a  and an  involved, and
both are powers of , let's try to get as much
as possible involving the number :

Let's first work only on the exponent



Use the change of base formula 

to change base  to base 



Write  as  and  as 



Use the rule  to rewrite
numerator and denominator:



Cancel the 's:



and we have just:



Use the rule  to rewrite the denominator:



or just



Now let's go back to the original problem, which was:



and replace the exponent with 



Rewrite the base  as 



Use the rule 



Use the rule  to rewrite the exponent:



Write  as 



Use the rule 

Final answer: 



--------------------------------



Again we notice there is a  and an  involved,
and both are powers of , let's try to get as much
as possible involving the number :

As before we first work only with the exponent:



We write  as  and  as 



Use the rule  to rewrite
numerator and denominator:



Cancel the 's





When no base is written, the base is assumed to be 



Write that fraction as a division:



Use the change of base formula:  on each to get them
to logs base 2.



Use the rule  to rewrite 



Invert the second fraction and change division to multiplication:



Cancel:



All that's left is 



Now let's go back to the original problem, which was:



and replace the exponent by the simpler 

 

Wow!  That just happens by chance to be the exact same
thing as we got in the first problem, so we just copy
the above from there on and, of course, it will have
the same final answer.

Rewrite the base  as 



Use the rule 



Use the rule  to rewrite the exponent:



Write  as 



Use the rule 

Final answer: 

 

Edwin