Answer

Verified

435.6k+ views

**Hint:**Compare the \[\log \left( {m + n} \right) = \log m + \log n\] with the fundamental law of logarithm, i.e., $\log \left( {mn} \right) = \log m + \log n$ and then find a relation between $m$ and $n$.

**Complete step-by-step answer:**

Given, \[\log \left( {m + n} \right) = \log m + \log n\]..........….. (1)

We know that the basic product law of logarithm is given by,

$\log \left( {mn} \right) = \log m + \log n$...........….. (2)

On comparing (1) and (2), we get-

$\log \left( {m + n} \right) = \log \left( {mn} \right)$

Now, $\log $on both sides cancel out and thus we get-

$m + n = mn$

$ \Rightarrow m = mn - n$

$ \Rightarrow m = n\left( {m - 1} \right)$

$ \Rightarrow \dfrac{m}{{m - 1}} = n$

**Hence, option (C) is the correct answer.**

**Note:**A logarithm can have any positive value as its base, but two log bases are more useful than the others: base-$10$ and base -$e$. If a $\log $ has no base written, we should generally assume that the base is $10$ as in our question. Also, the $\log $of both sides can be cancelled, only when the bases of both the $\log $ are equal.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The mountain range which stretches from Gujarat in class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths