Question

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★ㅤ$\sf{\dfrac{\dfrac{3}{2} log 3 + log \sqrt{8} + log \sqrt{125} }{log 2 + log 3 + log 5}}$​

Answer 1

Answer:

3/2

Step-by-step explanation:

${\dfrac{\dfrac{3}{2} log 3 + log \sqrt{8} + log \sqrt{125} }{log 2 + log 3 + log 5}}$

Can be written as :

$\dfrac{ log ({3}^{ \frac{3}{2} } \times {2}^{ \frac{3}{2} } \times {5}^{ \frac{3}{2} })}{ log(2 \times 3 \times 5) } \\ \dfrac{ log( {30}^{ \frac{3}{2} } ) }{ log(30) } \\ log_{30}( {30}^{ \frac{3}{2} } ) = \dfrac{3}{2}$

Using laws:

$log(x) + log(y) = log(xy)$

$log( {x}^{y} ) = y log(x)$

$\dfrac{ log(x) }{ log(y) } = log_{y}(x)$