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Evaluate $\log_\frac{1}{3}9$.

 Dec 18, 2014

Best Answer 

 #1
avatar+130511 
+5

In exponential form, this says

(1/3)x = 9 

Note that 1/3  = 3-1 and 9 = 32   so we can write

(3-1)x  = 32

3-x = 32    and, equating exponents, we have

-x  = 2     so   x = -2

So

log1/3 9 = -2

 

 Dec 18, 2014
 #1
avatar+130511 
+5
Best Answer

In exponential form, this says

(1/3)x = 9 

Note that 1/3  = 3-1 and 9 = 32   so we can write

(3-1)x  = 32

3-x = 32    and, equating exponents, we have

-x  = 2     so   x = -2

So

log1/3 9 = -2

 

CPhill Dec 18, 2014

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