L o g 5 4 ∗ l o g 6 5 + l o g 11 3 ∗ l o g 6 121 {\displaystyle Log_{5}4*log_{6}5+log_{11}3*log_{6}{121}}
מתבססת באמצעות נוסחת המעבר כאשר מעבירים לבסיס 11: l o g 11 4 l o g 11 5 ∗ l o g 11 5 l o g 11 6 + l o g 11 3 ∗ l o g 11 121 l o g 11 6 = 2 l o g 11 4 l o g 11 6 + l o g 11 3 ∗ l o g 11 11 2 l o g 11 6 = 2 L o g 11 4 + l o g 11 3 ∗ 2 l o g 11 11 = 2 l o g 11 6 L o g 11 4 + l o g 11 3 2 = 2 l o g 11 6 L o g 11 ( 4 ∗ 3 2 ) = 2 l o g 11 6 L o g 11 36 = 2 l o g 11 6 L o g 11 6 2 = 2 l o g 11 6 2 l o g 11 6 = 2 l o g 11 6 {\displaystyle {\begin{aligned}{\frac {log_{11}4}{log_{11}5}}*{\frac {log_{11}5}{log_{11}6}}+log_{11}3*{\frac {log_{11}121}{log_{11}6}}=2\\{\frac {log_{11}4}{log_{11}6}}+log_{11}3*{\frac {log_{11}11^{2}}{log_{11}6}}=2\\Log_{11}4+log_{11}3*2log_{11}11=2log_{11}6\\Log_{11}4+log_{11}3^{2}=2log_{11}6\\Log_{11}(4*3^{2})=2log_{11}6\\Log_{11}{36}=2log_{11}6\\Log_{11}6^{2}=2log_{11}6\\2log_{11}6=2log_{11}6\\\end{aligned}}}
מתבססת על הנוסחה L o g 5 5 ∗ l o g 6 4 + l o g 11 121 ∗ l o g 6 3 = 2 L o g 6 4 + 2 l o g 11 11 ∗ l o g 6 3 = 2 L o g 6 2 2 + 2 ∗ 1 ∗ l o g 6 3 = 2 2 L o g 6 2 + 2 l o g 6 3 = 2 2 ( l o g 6 2 + l o g 6 3 ) = 2 2 l o g 6 ( 2 ∗ 3 ) = 2 2 l o g 6 6 = 2 2 = 2 {\displaystyle {\begin{aligned}Log_{5}5*log_{6}{4}+log_{11}121*log_{6}3=2\\Log_{6}4+2log_{11}11*log_{6}3=2\\Log_{6}2^{2}+2*1*log_{6}3=2\\2Log_{6}2+2log_{6}3=2\\2(log_{6}2+log_{6}3)=2\\2log_{6}(2*3)=2\\2log_{6}6=2\\2=2\\\end{aligned}}}