a) [tex]E=\frac{\log_7x^2}{\log_8x^2}=\frac{\log_7x^2}{\frac{\log_7x^2}{\log_78}}=\log_7x^2\cdot\frac{\log_78}{\log_7x^2}=\log_78[/tex].
b) [tex]E=\frac{\log_2x+\log_2\sqrt{x}}{\log_3x+\log_3\sqrt{x}}=\frac{\log_2(x\sqrt{x})}{\log_3(x\sqrt{x})}=\frac{\log_2(x\sqrt{x})}{\frac{\log_2(x\sqrt{x})}{\log_23}}=\log_2(x\sqrt{x})\cdot\frac{\log_23}{\log_2(x\sqrt{x})}=\log_23[/tex].
