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log 1000

Answer
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Hint: We will be using the concepts of logarithmic function to solve the problem. We will first write 1000 as an exponent of 10 then we will use the logarithmic identities to further simplify the problem.

Complete step-by-step answer:
Now, we have to expand log 1000. So, now we will first express 1000 as 10n where n is any integer. So, we have,
1000=10n(10×10×10)=10n103=10nn=3
Therefore, we have 1000=103.
Now, we know the logarithmic identities that,
logabn=nlogab
So, now we have,
log1000=log103=3log10
So, log 1000 can be expanded as 3log10.

Note: To solve these type of questions it is important to note that we have to used logarithmic identity that logabn=nlogab. Also, it should be noted that 1000 can be written as 103, so the problem gets simplified. Also, there is an alternate method:
log1000=log(10×10×10)=log10+log10+log10=3log10
We have used the identity that logab=loga+logb.
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