Question

Express as single logarithm 3 log 7 - 2 log 5 + 3 log 2

Answer 1

Answer:

log(2744/125 ) is the correct answer of the given question

Answer 2

Answer:

$\displaystyle \implies\dfrac{\log343}{\log200}$

Explanation:

Given :

3 log 7 - 2 log 5 + 3 log 2

We have to write in single logarithm form

Here we will use two concept

$\displaytext{1. \log m+\log n=\log mn \ ..(i) }\\\\\displaytext{2. \log m-\log n=\log \dfrac{m}{n} \ ...(ii) }\\\\\displaytext{3. a \log m=\log m^a \ ...(iii) }$

Now

$\displaystyle \text{3 log 7 - 2 log 5 + 3 log 2}\\\\\displaystyle \text{From (iii) we can write it as}\\\\\displaystyle \log7^3-\log5^2+\log2^3\\\\\displaystyle \implies\log343-\log25+\log8\\\\\displaystyle \text{From (i) we can write it as}$

$\displaystyle \implies\log343-\log25\times 8\\\\\displaystyle \implies\log343-\log200\\\\\displaystyle \text{From (ii) we can write it as}\\\\\displaystyle \implies\dfrac{\log343}{\log200}$

Thus we get answer.