What is the answer to [tex] \log_{1/3} 27 [/tex]?
Answer (2)
l o g 3 1 27 = l o g 3 1 3 3 = 3 ⋅ l o g 3 1 3 = 3 l o g 3 1 ( 3 1 ) − 1 = − 1 ⋅ 3 l o g 3 1 3 1 = − 3
The logarithm lo g 1/3 27 simplifies to − 3 after converting 27 to a power of 3 and using logarithmic properties. Specifically, 27 = 3 3 and lo g 1/3 ( 3 ) = − 1 . Thus, lo g 1/3 27 = 3 ⋅ ( − 1 ) = − 3 .
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