[tex]\text{Given that,}\\\\\log_b x =2,~~ \log_b y=5,~~ \log_b z = 4\\\\\\\log_b(x\cdot y)\\\\=\log_b x + \log_b y~~~~~~~~~~~~~~~;[\log_b(MN) = \log_b M+ \log_b N ] \\\\=2+5\\\\=7\\\\\\\log_b\left( \dfrac{xy^2}{z^2}\right)\\\\=\log_b (xy^2) - \log_b z^2~~~~~~~~~~;\left[\log_b\left(\dfrac MN \right) = \log_b M - \log_b N \right] \\\\=\log_b x +\log_b y^2 - 2\log_b z\\\\=\log_b x + 2 \log_b y - 2 \log_b z\\\\=2+2 \cdot5 - 2 \cdot 4\\\\=2+10-8\\\\=10-6\\\\=4[/tex]
