[tex]\frac{log_26\cdot log_36}{log_26+log_36}=\frac{\frac{log6}{log2}\cdot\frac{log6}{log3}}{\frac{log6}{log2}+\frac{log6}{log3}}=\frac{\frac{log^26}{log 2\cdot log 3}}{\frac{log 6\cdot log 3}{log 2\cdot log 3}+\frac{log 6\cdot log2}{log 2\cdot log 3}}=\\\\\\\frac{\frac{log^26}{log 2\cdot log 3}}{\frac{log 6\cdot log 3+log 6\cdot log2}{log 2\cdot log 3}}=\frac{log^26}{log 2\cdot log 3}\cdot\frac{log 2\cdot log 3}{log 6\cdot log 3+log 6\cdot log2}=[/tex]
[tex]\frac{log^26}{log 6\cdot log 3+log 6\cdot log2}=\frac{log^26}{log 6\cdot (log 3+log log2)}=\frac{log^26}{log 6\cdot log (3\cdot2)}=\frac{log^26}{log 6\cdot log 6}=1[/tex]
