[latex]\a) \ \frac{log_56}{log_5216}=frac{log_56}{log_56^3}=frac{log_56}{3*log_56}=frac13 \ \b) \ \log_37*frac{log_3frac{sqrt3}{3}}{log_37}=log_3frac{sqrt3}{3}=xiff 3^x=log_3frac{sqrt3}{3} \ \3^x=3^{frac12-1} \ \3^x=3^{-frac12} \ \x=-frac12[/latex]
a) [latex] frac{log_{5}6}{log_{5}6^{3}} = frac{log_{5}6}{3log_{5}6}= frac{1}{3} [/latex] b) [latex]log_{7} frac{ sqrt{3} }{3} = frac{log_{3} frac{ sqrt{3} }{3} }{log_{3}7} = frac{log_{3} sqrt{3}-log_{3}3 }{log_{3}7}=frac{ frac{1}{2} -1 }{log_{3}7}= -frac{ frac{1}{2} }{log_{3}7}= - frac{1}{2log_{3}7} [/latex] [latex]log_{3}7 * log_{7} frac{ sqrt{3} }{3} = [/latex][latex]log_{3}7*(- frac{1}{2log_{3}7} )= - frac{1}{2} [/latex]
