Simplify. 4^log 4^(7)

Question

Simplify. 4^log 4^(7) 

 

 

 

4^log 4^(7) = ?

 

 

 

Answer 1

Do you mean this: 4^log_4(7) where _4 means subscript 4, i.e.,base 4?

 

Then let n = 4^log_4(7)

 

Take log base 4 of both sides:

 

log_4(n) = log_4(4^log_4(7))

 

Use Power Rule:

 

log_4(n) = (log_4(7))*log_4(4)

 

log_4(n) = (log_4(7))*1

 

Same base on both sides so:

 

n = 7

Answer 2

 4 ^ log 4 ^ 7 = 4 ^( 7log 4) = 4 ^( 7* .6) = 4 ^ (4.2 ) = 337 .80

 

   Calculator :

                       4 ^ ( log(4^7)= 344.61