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Compute \(\log_{1/2} 16 - \log_9 27\).

 Dec 3, 2019
 #1
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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

 

 

cool cool cool

 Dec 3, 2019

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