Question

log 81/8 -2 log 3/2 + 3log 2/3 +log 3/4 =0​

Answer 1

Answer:

4log3-3log2-2log3-2log2+3log2-3log3+log3-2log2

Step-by-step explanation:

=-4log2

Answer 2

$5\log 3+4\log 2 =0$is the required solution.

Step-by-step explanation:

We have,

$\log \dfrac{81}{8} -2\log \dfrac{3}{2} +3\log \dfrac{2}{3} +\log \dfrac{3}{4}=0$

⇒ $\log \dfrac{3^{4} }{2^{3} } -2\log \dfrac{3}{2} +3\log \dfrac{2}{3} +\log \dfrac{3}{4}=0$

⇒ $4\log 3- 3\log 2 - 3\log 3+2\log 2 +3\log 2+ 3\log 3 +\log 3 +2\log 2 =0$

[ ∵ $\log mn=\log m+\log n$, $\log \dfrac{m}{n} =\log m-\log n$ and $\log a^{m} =m\log a$]

⇒$5\log 3+4\log 2 =0$

Hence, $5\log 3+4\log 2 =0$is the required solution.