Question

15 puntos ayuden:,v con procedimiento porfa

Answer 1

Respuesta:

$m=49$ b)49

Explicación paso a paso:

$\left(\sqrt{3}\right)^{\log _{\sqrt{3}}\left(m\right)}=16^{\log _4\left(7\right)}\\\left(\sqrt{3}\right)^{\log _{\sqrt{3}}\left(m\right)}=3^{\frac{1}{2}\log _{\sqrt{3}}\left(m\right)}\\3^{\frac{1}{2}\log _{\sqrt{3}}\left(m\right)}=16^{\log _4\left(7\right)}\\\ln \left(3^{\frac{1}{2}\log _{\sqrt{3}}\left(m\right)}\right)=\ln \left(16^{\log _4\left(7\right)}\right)\\\ln \left(3^{\frac{1}{2}\log _{\sqrt{3}}\left(m\right)}\right)=\frac{1}{2}\log _{\sqrt{3}}\left(m\right)\ln \left(3\right)$

$\frac{1}{2}\log _{\sqrt{3}}\left(m\right)\ln \left(3\right)=\ln \left(16^{\log _4\left(7\right)}\right)\\\ln \left(16^{\log _4\left(7\right)}\right)=\log _4\left(7\right)\ln \left(16\right)\\\frac{1}{2}\log _{\sqrt{3}}\left(m\right)\ln \left(3\right)=\log _4\left(7\right)\ln \left(16\right)$

$\log _{\sqrt{3}}\left(m\right)=\frac{8\ln \left(2\right)\log _4\left(7\right)}{\ln \left(3\right)}\quad \Rightarrow \quad \:m=\sqrt{3}^{\frac{8\ln \left(2\right)\log _4\left(7\right)}{\ln \left(3\right)}}\\m=\left(\sqrt{3}\right)^{\frac{8\ln \left(2\right)\log _4\left(7\right)}{\ln \left(3\right)}}\\\\m=49$