Question

if log36.2=1.5587 ,what is the characteristics of
log=36.2

Answer 1

sir.. please help me

Answer 2

is the answer 1?
how to get this? what's the solution sir?

Answer 3

Every common logarithm has two main parts:

i). an integer part called the "characteristic", and
ii). a decimal part called the "mantissa".

The characteristic of every common logarithm depends on the argument number N. If N > 1, the characteristic is one less than the number of digits in the whole number portion of the argument number N. If 0 < N < 1, the characteristic is negative and one greater than the number of leading zeros in the decimal place of the argument N. For example,

Suppose N = 2 536.002 (a number greater than 1). Then

log (2 536.002) = log (1000 x 2.536 002)

log (2 536.002) = log (1000) + log (2.536 002)

[∵ log (xy) = log x + log y]. Continuing

log (1000) + log (2.536 002) = 3 + log (2.536 002)

∴ the characteristic of log (2 536.002) is 3.

Now suppose N is a number between 0 and 1. Let's say

N = 0.011 235.

log (0.011 235) = log (1.112 35 x 0.01)

log (0.011 235) = log (1.112 35) + log (0.01)

log (0.011 235) = log (1.112 35) + (-2)

∴ the characteristic of log (0.011 235) is -2 [∵ 10ˆ-2 = 0.01].

Now that we've built character, let's find the mantissa. This one's too easy. Let's take a look at the above examples one more time. Recall

log (2 536.002) = 3 + log (2.536 002)

∴ log (2.536 002) = 0.404 149 591 713 ... is the mantissa


@02231985 as a teacher I won't simply give you the answer. I will teach you and help you learn. I wrote the short lesson above for you, now you read it and try it yourself.

Answer 4

sir?
what's the N here?
the 36.2 or the1.5587

Answer 5

i think 36.2

Answer 6

Read the lesson carefully and you shall see that the N is the argument or the antilogarithm. Thus in log (36.2), N = 36.2.

Answer 7

yeah
i'm right

Answer 8

Yes you are smart!!!!!!! :)

Answer 9

log (1000 )
but i'm confused. . where did you get that?
is that from
\[\log {2536.002} =1000\]

Answer 10

or is it constsant for numbers greater than1

Answer 11

Because log (2536.002) = log (1000 X 2.536.002)

Answer 12

yeah i saw
its like it is expanded of the simpler theory of log (xy) = log x + log y
but sir. .
the x there is 1000
is 1000 constant in determining characteristics of numbers greater than 1

Answer 13

Let me explain again, but in different terms. To find the mantissa, write the argument in scientific notation form, then the mantissa will be the power of 10.

Thus if given log (2536.002), the argument is 2536.002. Now written in scientific notation,

2536.002 = 2.536 002 X 10³

Here the power of 10 is 3.

∴ the mantissa is 3.

Answer 14

Oh I see you already got it! Great! Good Work!!

Answer 15

ahhhhh
like in scientific notations

Answer 16

my answer above is 1
is it right sir?

Answer 17

Sorry, I mean characteristic, NOT mantissa!

Answer 18

sir? ? ?
is my answer right?

Answer 19

Yes your answer of 1 is correct!

Log (36.2) = log (10 X 3.62)

log (36.2) = log 10 + log (3.62)

log (36.2) = 1 + log (3.62)

∴ the characteristic is 1.

OR

36.2 in scientific notation is 3.62 X 10. Since we have the first power of ten, the characteristic is 1.


Good job @02231985

Answer 20

sir can i ask another question?

Answer 21

thank you @calculusfunctions

Answer 22

Welcome! Sure you may ask but I have to go soon.

Answer 23

yes sir.
hm
The half-life of a radioactive substance is 5 minutes. how much of an original mass of 100 grams remains after half an hour?

Answer 24

You may use the universal half-life formula\[M =M _{0}\left( \frac{ 1 }{ 2 } \right)^{\frac{ t }{ h }}\]where\[M _{0}\] is the initial mass present,\[h\]is the time it takes for the initial mass to reach half of it,\[t\]is the time it takes the substance to decay to the final mass, and \[M\]is the final mass.

Answer 25

You may also apply calculus but I presume you may not have learned calculus yet.

Answer 26

One quick note: t and h must have the same unit of time.

Answer 27

@02231985 are you there? If you understand, then please reply.

Answer 28

sir . . i'm confused on where I could substitute the 5 in t or h?
but sir even i Substitute those two :
t=30
h=5

Answer 29

Yes you have it right!

t = 30 minutes
h = 5 minutes

because the question very clearly stated that the substance has a half life of 5 minutes.

Answer 30

i have used that also. . . its just that \[M _{0} is N _{0}\]
the answers i got was wrong
it was not in the choices sir. .

Answer 31

So did you get it?

Answer 32

\[100(\frac{ 1 }{ 2 })^{\frac{ 30 }{ 5}}\]

Answer 33

Yes M equals the expression you have above. So what do you get for M?

Answer 34

sir should i get first the (12)305

Answer 35

Remember the Order of Operations (BEDMAS) Always!!

Answer 36

(\[\frac{ 1 }{ 2})^{6}\]

Answer 37

Yes! Then multiply by 100.

Answer 38

So what is your final mass?

Answer 39

\[1\frac{ 9 }{ 16 }\]

Answer 40

No. It is not a mixed fraction!

Answer 41

1.5625

Answer 42

100 X (1/2)ˆ6

Answer 43

1.5625

Answer 44

Yes! That is the final mass! 1.5625 grams. Very Good!

Answer 45

ah yes
SIR is it morning there?

Answer 46

Sorry, your mixed fraction was right but what I meant to say is that for this type of question, express your answer as a decimal. Good Job!

Answer 47

yes sir

Answer 48

Yes it is! Where are you from?

Answer 49

philippines sir. .

Answer 50

I see. I'm in Canada.

Answer 51

Two sides of a triangular plot of land have lengths of 400ft and 600 ft. The measurement of the angle between those sides is 46degrees 20. Find the perimeter of the plot

Answer 52

ahh ok sir. .
thank you very much sir. .

Answer 53

I have to go now, otherwise I'd definitely help. But quickly, what do you mean by 46 degrees 20? Do you mean 46 degrees and 20 minutes? Please be clear.

Answer 54

yes sir

Answer 55

sir can i leave message to you
about those questions. . .
i will just read the lesson sir. . .

Answer 56

Yes what? 46 degrees and 20 minutes?

Answer 57

yes sir 46 degrees and 20 minutes

Answer 58

OK so quickly before I go I'll help you with this last one. Are you ready?

Answer 59

yes sir

Answer 60

OK first to convert minutes into degrees, multiply the minutes by 1/60.

Now draw and label the triangle using the draw feature below and show me quickly.

Answer 61

1/3

Answer 62

20 minutes equals 20/60 or 0.333333.......... degrees. Thus 46 degrees and 20 minutes equals 46.33 degrees approximately. Understand? Now please show me your diagram.