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Compute \(\log_{1/125} (25 \sqrt[3]{25})\)

 Dec 24, 2019
 #1
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In exponential form  we have that

 

(1/125)^x  = 25∛25

 

[5^(-3)]^x  =  25 ^(4/3)

 

5^(-3x)  = (5^2)^(4/3)

 

5^(-3x) = 5^(8/3)      solve for the exponents

 

-3x =  (8/3)      divide both sides by  -3

 

x=  -8/9

 

 

cool cool cool

 Dec 24, 2019
edited by CPhill  Dec 24, 2019

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