Question

Find the value with the help of logarithem tables.
3614 x 46.282
102.32 x 16.82
​

Answer 1

Answer:

Let x=5872×0.058

Taking log both sides, we have

logx=log(5872×0.058)

logx=log5872+log0.058(∵logab=loga+logb)

logx=log(58.72×10

2

)+log(58×0

−3

)

logx=log58.72+2+log58−3(∵log10=1)

⇒1+logx=log58.72+log58

Using log table, we get

log58.72=1.77

log58=1.76

∴1+logx=1.77+1.76

⇒logx=3.53−1

⇒logx=2.53

⇒x=Antilog(2.53)=338.84

Therefore,

5872×0.058≈338.84

Answer 2

Answer: 167200

             1721

Step-by-step explanation:

3614 x 46.282

$lg P=lg(3614$ x 46.282)

If numbers multiply, logarithms will be added.

$lg P=lg3614 + lg46.282$

(First find the logarithmic value for 3614.  To see this,

1.In the first column search for the first 2 digits of the number. (3614)

First 2 digits 36

2. In the second column search for the third digit of the number. (1)

3. Find the value that is written on the column of 1 in the row of 36.

Which is 5575

4. Next search for the fourth digit in the last section called mean differences   along the same row of 36.

5

Now you have to add the number which you obtained from the second section and last section

5575 + 5 = 5580

5. you have to remember that originally the decimal point should have to be after first digit. Which means in 3614 decimal point should have been beside 3. (3.614)

6. But the decimal is situated after the digit 4. (If the decimal is not shown, then it is available at the end of the number.)

Decimal point has gone 3 points backwards.

So we can write 3614 as 3.5580

In this same manner you have to see the logarithmic value for 46.282 also.

$lg P=lg3614 + lg46.282$

       =3.5580 + 1.6653

       =5.2233

To find the final value you have to see the antilog

$antilog 5.2233$

01. To find the antilog search for the value 2233 in the second section of the logarithmic table.

02.If 2233 is not available take a number which is lower than it.

03. Here the number lower than 2233 is 2227.

2227 is in the row of the number 16 and the column of the number 7.

we still need 6 more to reach the number 2233. (2233-2227)

So you have to see in the last section, in which column, 6 is situated. (along the row of the number 16) (If 6 is not there any nearest value lower than 6)

5 is in the column of the number 2

So, digits for the antilog is 1.672. (decimal point would always be after first digit)

Since 5. is at the front (5.2233), we have to multiply 1.672 by $10^{5}$

1.672 x $10^{5}$

=167200

__________________________________________________________

102.32 x 16.82

​$lg P=lg(102.32$ x 16.82)

      =$lg 102.32 + lg 16.82$

      =2.0098 + 1.2258

      =3.2356

$antilog 3.2356$

    1.721 x $10^{3}$

1721

Hope it was understandable.

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