Question

Please answer 4th question

Answer 1

Step-by-step explanation:

check this image.

here is your answer.

Answer 2

$\red{ANSWER}$

$\rm{a^{x}=2^{\frac{3}{2}}}$

$\bold{\pink{EXPLANATION}}$

$\underline{\mathbb{GIVEN\:QUESTION\:IS}}$

$\rm{\log_{a}\left(\frac{\left(13\right)^2}{\sqrt{2^3}\times5}\right)=2\log_{a}13-\log_{a}5-x}$

$\underline{\mathbb{SOLUTION}}$

$\rm{\log_{a}\left(\frac{\left(13\right)^2}{\sqrt{2^3}\times\:5}\right)=\log{a}\left(13\right)^2-\log_{a}5-x}$

$\boxed{\pink{\log_{x}\:y^n=n\log_{x}y}}$

$\rm{\log_{a}\left(\frac{\left(13\right)^2}{\sqrt{2^3}\times5}\right)=\left(\log_{a}\frac{\left(13\right)^2}{5}\right)-x}$

$\boxed{\pink{\log_{a}\:m-\log_{a}\:n=\log_{a}\:\left(\frac{m}{n}\right)}}$

$\rm{\log_{a}\left(\frac{\left(13\right)^2}{\sqrt{2^3}\times5}\right)-\left(\log_{a}\frac{\left(13\right)^2}{5}\right)=-x}$

$\rm{\log_{a}\left(\frac{\left(13\right)^2}{\sqrt{2^3}\times5}\times\frac{\left(13\right)^2}{5}\right)=-x}$

$\boxed{\pink{\log_{a}m-\log_{a}n=\log_{a}\left(\frac{m}{n}\right)}}$

$\rm{log_{a}\:\left(2^{\frac{-3}{2}}\right)=-x}$

$\rm{\frac{-3}{2}\log_{a}2}=-x$

$\boxed{\pink{\log_{x}\:y^n=n\log_{x}y}}$

$\rm{log_{a}\:\left(2^{\frac{3}{2}}\right)=x}$

$\boxed{\pink{\rm{IF\:\log_{x}\:y=z\:\:\:Then\:\:y=x^z}}}$

$\rm{2^{\frac{3}{2}}=a^x}$

$\rm{a^x=2^{\frac{3}{2}}}$

$\therefore$$\rm{a^x=2^{\frac{3}{2}}}$

$\rm{\pink{HENCE,\:OPTION\:'A'\:IS\:CORRECT}}$