help with log

log _1/2  16 -  log ₉  27      

Note that  in exponential form

(1/2)^(-4)  =  1 / (1/2)^4  =  1  /(1/16)   = 16

So....the first expression evaluates to -4

And

9^x  = 27

(3^2)^x  = 3^3

(3)^(2x)  = 3^3      the bases are the same.....solve for the exponents

2x= 3    divide both sides  by  2

x  = 3/2

So.....the second expression evaluates to 3/2

So

-4  - (3/2)   =

-8/2  - 3/2  =

-11/2  = -5.5