Question

If log (0.0007392)=-3.1313 , then find log(73.92)

Answer 1

Given:

Given value is, $log (0.0007392)=-3.1313$.

To find:

We should find the value of $log(73.92)$.

Solution:

We can find the value of $log(73.92)$, by doing some manipulations in given value.

Consider the given value,

$\Rightarrow log (0.0007392)=-3.1313$

Now, multiply with 100000 and divide with 100000 to the $0.0007392$.

$\Rightarrow log (0.0007392\times \frac{100000}{100000} )=-3.1313$

Multiplying the terms,

$\Rightarrow log ( \frac{0.0007392\times100000}{100000} )=-3.1313$

Simplifying the terms,

$\Rightarrow log ( \frac{73.92}{100000} )=-3.1313$

We know that, $log\frac{a}{b} =log\ a-log\ b$.

Now apply the above formula.

$\Rightarrow log \ {73.92}-log\ {100000}=-3.1313$

Rearranging the terms,

$\Rightarrow log \ {73.92}=-3.1313+log\ {100000}$

$\Rightarrow log \ {73.92}=-3.1313+log\ {10^5}$

We know that, $log\ a^m = m\ log\ a$.

$\Rightarrow log \ {73.92}=-3.1313+5\ log\ {10}$

But the value of $log \ 10$ is equal to 1.

$\Rightarrow log \ {73.92}=-3.1313+5\times1$

Simplifying the terms,

$\Rightarrow log \ {73.92}=-3.1313+5$

$\Rightarrow log \ {73.92}=1.8687$

Hence, we got the required value.

Therefore, the value of $log \ {73.92}$ is equal to $1.8687$.

Answer 2

SOLUTION

GIVEN

log (0.0007392) = - 3.1313

TO DETERMINE

log(73.92)

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm

$\sf{}1. \: \: \log (ab) = \log a \: + \log b$

$\sf{}2. \: \: \log( {a}^{m} ) = m \log a$

EVALUATION

Here it is given that

$\sf{} \log (0.0007392) = - 3.1313 \: \: \: ......(1)$

Now

$\sf{} \log (73.92)$

$= \sf{} \log (0.0007392 \times {10}^{5} )$

$= \sf{} \log (0.0007392 ) + \log ({10}^{5} ) \: \: using \: formula \: 1$

$= \sf{} \log (0.0007392 ) + 5 \log ({10} ) \: \:( using \: formula \: 2)$

$= \sf{} \log (0.0007392 ) + 5 \: \: ( \because \log(10) = 1)$

$\sf{} = - 3.1313 + 5$

$\sf{} = 1.8687$

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