SOMEONE MAJOR HELP!!!!! ANALYSIS & FUNCTIONS! 10 points for best answer!?

Question

need major help! Studying for a final and I'm stuck on only these!!!please help me pass!!!

1.
Evaluate the exponential expression
3^2 times 3^-3

2^7/2^2

2.
Find the exact solution to the equation.
log 4 x=5

Answer 1

1) Given expresson 3^2 times 3^-3 can be writen as 3^2 X 3^-3

                                                                                         = 3^(2-3)  [ If bases are equal then powers are added ]

                                                                                         = 3^-1       [ Since a^-1 = 1/a ]

                                                                                         = 1/3.

     And 2^7/2^2 = 2^7-2    [ If bases are equal on division then powers are subtracted ]

                           = 2^5

                           = 32.

 

Answer 2

2) Given equation is log4x = 5

  [ If loga=b then ]

100000 = 4x

x = 100000/4

x = 25000

Therefore the exact solution is 25000.