[tex]d) \ log_{\frac{1}{9}}log_{4}64 = log_{\frac{1}{9}}log_{4}4^{3} = log_{\frac{1}{9}}3 = log_{\frac{1}{9}}(\frac{1}{9})^{-\frac{1}{2}} = -\frac{1}{2}\\\\\\e) \ log_{\sqrt{3}}log_{\frac{1}{2}}\frac{1}{8} = log_{\sqrt{3}}log_{\frac{1}{2}}(\frac{1}{2})^{3}=log_{\sqrt{3}}3 = log_{\sqrt{3}}(\sqrt{3})^{2} = 2[/tex]
[tex]f) \ log_{\sqrt{5}}log_{2}32 = log_{\sqrt{5}}log_{2}2^{5}} = log_{\sqrt{5}}5 = log_{\sqrt{5}}(\sqrt{5})^{2}} = 2[/tex]
