Based on the definition of logarithms, what is \log_{10}1000

Trent Carpenter

Trent Carpenter

Answered question

2021-10-10

Based on the definition of logarithms, what is log101000

Answer & Explanation

Malena

Malena

Skilled2021-10-11Added 83 answers

Step 1
We have to find the exact value of the logarithm
log101000
logc(ab)=blogc(a)
logc(c)=1
Step 2
The first property says that irrespective of the base of the logarithm if we have an exponent of a number in the logarithm then index of the number can be taken out of the logarithm without changing the base.
The second property says that logarithm of a number in which the base of logarithm is the number itself is always equal to one.
Step 3
Thus using first property we can simplify the given logarithm as shown:
log101000=log10(10)3
=3log1010 Step 4
Next using the second property of logarithm we can further simplify this logarithmic expression as shown:
log101000=3log1010=3
Answer:
log101000=3
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-03Added 2605 answers

Answer is given below (on video)

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