Note: Not available

Note: Given Expression `= log_xyz (xy) + log_xyz (yz) + log_xyz (zx)` `= log_xyz (xy xx yz xx zx)` `= log_xyz (xyz)^2` `= 2 log_xyz (xyz)` `= 2 xx 1` `2`

Note: Given Exp. `= 1/(log_a bc + log_a a) + 1/(log_b ca + log_b b) + 1/(log_c ab + log_c c)` `= 1/(log_a (abc)) + 1/(log_b (abc) + 1/(log_c (abc)` `= log_abc a + log_abc b + log_abc c` `= log_abc (abc) = 1.`

Note: `log_2 [ log_3 (log_2 x)] = 1` `= log_2 2` `⇔ log_3 (log_2 x)` `= 2 ⇔ log_2 x` `= 3^3 = 9 ⇔ x = 2^9` `= 512.`

Note: Given Expression `= (log 9)/(log 4) xx (log 2)/(log 3) [:. log_5 5 = 1]` `= (log 3^2)/(log 2^2) xx (log 2)/(log 3)` `= (2 log 3)/(2 log 2) xx (log 2)/(log 3) = 1`

Note: `log_10^(1.5)` `= log_10 (3/2)` `= log_10^3 - log_10^2` `= (0.4771 - 0.3010)` `= 0.1761.`

Note: `log_2 10` ` = 1/(log_10 2)` `= 1/.3010` `= 10000/3010` `= 3.3222.`

Note: Given Expression `= log_60 3 + log_60 4 + log_60 5` `= log_60 (3 xx 4 xx 5)` `= log_60 60` `= 1`

Note: Given Expression `= (log 4)/(log 3) xx (log 5)/(log 4) xx (log 6)/(log 5) xx (log 7)/(log 6) xx (log 8)/(log 7) xx (log 9)/(log 8)` `= (log 9)/(log 3)` `= (log 3^2)/(log 3)` `= (2 log 3)/(log 3)` `= 2`

Note: `log_10 5 = log_10 (10/2)` `= log_10 10 - log_10 2` `= 1 - log_10 2` `= (1 - 0.3010)` `= 0.6990`.