+0

# Do you notice a difference in these answers?

0
266
2
+152

Observe these problems:

21. log 3.000

23. log 30.00

25. log 300.00

27. log 3000

29. log (3 x 10^12)

What pattern do you notice in the answers from these?

#1
+85718
+10

These answers all have the same decimal part .....the only diffenence is in the integer part of their evaluation. The integer part tells us the exponent on "10" when we write the given antilog in scientific notation.

Thus

3 = 10^.477 = 3 x 10^0

30 = 10^1.477 = 3 x 10^1

etc.

CPhill  Jan 31, 2015
Sort:

#1
+85718
+10

These answers all have the same decimal part .....the only diffenence is in the integer part of their evaluation. The integer part tells us the exponent on "10" when we write the given antilog in scientific notation.

Thus

3 = 10^.477 = 3 x 10^0

30 = 10^1.477 = 3 x 10^1

etc.

CPhill  Jan 31, 2015
#2
+92206
+5

Yes :)

log 3.000 = log3

log 30.00 = log(10*3)=log10+log3=1+log3

log 300.00= log(100*3)=log100+log3=2+log3

log 3000= log(1000*3)=log1000+log3=3+log3

log (3 x 10^12)= log(10^12*3)=log10^12+log3=1,000,000,000,000+log3

Melody  Jan 31, 2015

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