Question

The simplified form of log(75/16) -2log(5/9) +log(32/343) is ?

Answer 1

Answer:

The simplified form is given by 5log3+log2-3log7

Explanation:

We have been given the expression

$\log(\frac{75}{16})-2\log(\frac{5}{9})+\log(\frac{32}{343})$

We can use the below logarithm formula to simplify the above expression

$\log(ab)=\log a +\log b\\\log (a/b)=\log a - \log b\\\\\log a^b= b \log a$

Use these properties, we have

$\log 75 -\log 16 -2\log 5 +2\log 9 +\log 32 - \log 343\\\\=\log(5^2 \times 3) -\log(2^4)-2\log 5 +2\log 3^2 +\log 2^5 -\log 7^3\\\\=2\log5+\log3-4\log2-2\log5+4\log3+5\log2-3\log7\\\\=5\log3+\log2-3\log7$

Therefore, the simplified form is given by 5log3+log2-3log7