Question

Simplify log81÷8+2log2/3-3log3/2+log3/4

Answer 1

Answer:

log=4/9

Step-by-step explanation:

Using Laws of Logarithms

Answer 2

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

Step-by-step explanation:

Given : Expression $\log \dfrac{81}{8}+2\log \dfrac{2}{3}-3\log \dfrac{3}{2} +\log \dfrac{3}{4}$

To find : Simplify the expression ?

Solution :

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

Re-write expression using logarithmic properties as,

$\log mn=\log m+\log n$

$\log \dfrac{m}{n} =\log m-\log n$

$\log a^{m} =m\log a$

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

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

$=0$

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

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