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If Logx (1 / 8) = - 3 / 2, then x is equal to 

A. - 4 
B. 4 
C. 1 / 4 
D. 10

off-topic
DarkCalculis  Feb 16, 2018
edited by DarkCalculis  Feb 16, 2018
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3+0 Answers

 #1
avatar
+1

Solve for x:

-log(8)/log(x) = -3/2

 

Take the reciprocal of both sides:

-log(x)/log(8) = -2/3

 

Multiply both sides by -log(8):

log(x) = (2 log(8))/3

 

(2 log(8))/3 = log(8^(2/3)) = log(4):

log(x) = log(4)

 

Cancel logarithms by taking exp of both sides:

x = 4

Guest Feb 16, 2018
 #2
avatar+86649 
+1

Remember, DC, that

 

log a  = b    in exponential form  is  10^b  = a

 

So

 

 Logx (1 / 8) = - 3 / 2   =

 

x^(-3/2)  =  1/8       take each side to the  (-2/3) power

 

x  =  (1/8)^(-2/3)    =   [ (1/8)^(1/3) ]^(-2)   =   ( 1 /  3√8  )^(-2)   =   (1/2)^(-2)

 

Note now that    (1/a)^(-m)  =  a^m

 

So

 

(1/2)^(-2)  =  (2)^2   =  4  =  x

 

 

 

cool cool cool

CPhill  Feb 16, 2018
 #3
avatar+179 
+1

thanks, CPhill I owe you one

DarkCalculis  Feb 16, 2018
edited by DarkCalculis  Feb 16, 2018

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