Answer: [tex]\log\dfrac{x^2z^2}{y}[/tex]
Step-by-step explanation:
Properties of logarithm:
[tex](i)\ \ n\log a = a^n\\\\ (ii)\ \ \log m +\log n =\log (mn)\\\\ (iii)\ \ \log m-\log n =\log\dfrac{m}{n}[/tex]
Consider,
[tex]2\log x-\log y+2 \log z\\\\ =\log x^2-\log y+\log z^2\ \ \ \ \text{[By (i)]}\\\\= \log x^2+\log z^2-\log y\\\\=\log(x^2z^2)-\log y\ \ \ \ [\text{By } (ii) ]\\\\=\log(\dfrac{x^2z^2}{y}) \ \ \ \ [\text{By (iii)}][/tex]
