How do I simplify \log (1/sqrt(1000))

tidones0r 2022-09-14 Answered
How do I simplify log ( 1 / 1000 )?
What I have done so far:
1) Used the difference property of logarithms
log ( 1 1000 ) = log ( 1 ) log ( 1000 )
2) Used the exponent rule for logarithm
log ( 1 ) 1 2 log ( 1000 )
I'm stuck at this point. Can someone explain why and what I must do to solve this equation?
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Answers (2)

Nancy Ewing
Answered 2022-09-15 Author has 3 answers
Hint:
1 1000 = 10 3 2 and log x a = a log x
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Marcus Bass
Answered 2022-09-16 Author has 2 answers
log 10 ( 1 1000 ) = log 10 ( 1 10 3 ) = log 10 ( 1 10 3 2 ) = log 10 ( 10 3 2 ) = 3 2
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