Question

find log(0.5679×0.0789/0.0073×0.123) by logarithm table

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Answer 1

Answer:

0.5679×0.0789/0.0073×0.123

Answer 2

The complete question is :

find  $\log( \frac{0.5679\times 0.0789}{0.0073\times0.123})$  by logarithm table

The value of the logarithmic expression $\log( \frac{0.5679\times 0.0789}{0.0073\times0.123})$  is 1.6982 as calculated using logarithm tables.

The expression is  $\log( \frac{0.5679\times 0.0789}{0.0073\times0.123})$

We will use the logarithmic properties to simplify the above expression.

We know the logarithmic multiplication rule as  : $\log (a\cdot b)= \log a+\log b$  

The logarithmic division rule is : $\log(\frac{x}{y} )=log x- \log y$

Now we will use these rules for the complex expression:

$\log( \frac{0.5679\times 0.0789}{0.0073\times0.123})\\\=\log 0.5679+\log 0.0789-\log0.0073-\log 0.123$

Now we will find the individual values of the logarithms using the logarithm tables:

log 0.5679

Here the mantissa = -1 (0.5679<0)

Characteristic (from the log table) = 0.7643

$\log 0.5679 = -1+0.7543 = -0.2457$

Similarly, we will find each logarithmic value.

log 0.0789

mantissa = -2

Characteristic = 0.8971

$\log 0.0789 =-2+0.8971=-1.1029$

log 0.0073

mantissa = -3

Characteristic = 0.8633

$\log 0.0789 =-3+0.8633=-2.1367$

log 0.123

mantissa = -1

Characteristic = 0.0899

$\log 0.123 =-1+0.0899=-0.9101$

$\log 0.5679+\log 0.0789-\log0.0073-\log 0.123\\\= -0.2457 + (-1.1029) - (-2.1367)-(-0.9101)\\\\=1.6982$

Now we will use these values :

$\log 0.5679+\log 0.0789-\log0.0073-\log 0.123\\\\\= -0.2457 + (-1.1029) - (-2.1367)-(-0.9101)\\\\=1.6982$

Therefore the value of the logarithmic expression is 1.6982.

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