
Expand the following:
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 where n is any integer. So, we have,
Therefore, we have .
Now, we know the logarithmic identities that,
So, now we have,
So, log 1000 can be expanded as .
Note: To solve these type of questions it is important to note that we have to used logarithmic identity that . Also, it should be noted that 1000 can be written as , so the problem gets simplified. Also, there is an alternate method:
We have used the identity that .
Complete step-by-step answer:
Now, we have to expand log 1000. So, now we will first express 1000 as
Therefore, we have
Now, we know the logarithmic identities that,
So, now we have,
So, log 1000 can be expanded as
Note: To solve these type of questions it is important to note that we have to used logarithmic identity that
We have used the identity that
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