Question

Plz answer the question

Answer 1

Answer:

Refer attachment!!!

Explanation:

Answer 2

$\star$ Identities used :

     $loga+logb+logc=log(abc)\\\\log_{10}10=1\\\\log_{10}1=0\\\\m.logn=logm^n$

$\star$ Explanation :

$\star$ 1 )

$\star$ Given ,

$a=log\frac{2}{3},b=log \frac{3}{5} ,c=2log\sqrt{\frac{5}{2} } =log\sqrt{(\frac{5}{2} )^2}=log\frac{5}{2} \\\\=>c=log\frac{5}{2}$

$\star$ Now ,

 $a+b+c=log\frac{2}{3}+log\frac{3}{5}+log\frac{5}{2}\\\\=>a+b+c=log(\frac{2}{3}*\frac{3}{5}*\frac{5}{2})\\\\=>a+b+c=log1\\\\=>a+b+c=0$

$\star$ 2 )

$log_{10}y+2log_{10}x=2\\\\=>log_{10}y+log_{10}x^2=2log_{10}10\\\\=>log_{10}y.x^2=log_{10}10^2$

$\star$ Now apply $log_{10}^{-1}$ to both sides , we get ,

$=>log_{10}^{-1}.log_{10}yx^2=log_{10}^{-1}.log_{10}10^2\\\\=>y.x^2=10^2\\\\=>y=(\frac{10}{x})^2$

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