General Mathematics

Question: The value of `log_2 (log_5 625)` is :
A
`2`

B
`5`

C
`10`

D
`15`

Note: Let `log_5 625 = x.` Then,`5^x = 625` `= 5^4 or x = 4.` Let `log_2 (log_5 625) = y.` Then,`log_2 (4) = y` `or 2^y = 4 = 2^2.` So,`y = 2.` :.`log_2 (log_5 625) = 2.`
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Question: The value of`(1/3 log_10 125 - 2log_10 4 + log_10 32)` is :
A
`0`

B
`4/5`

C
`2`

D
`1`

Note: `1/3 log_10 125 - 2log_10^4 + log_10^32` `= log_10 (125)^1/3 - log_10 (4^2) + log_10 ^32` `= log_10 16 + log_10^32` `= log_10 ((5 xx 32)/(16))` `= log_10^10` `= 1.`
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Question: `[log (a^2/(bc)) + log (b^2/(ac)) + log (c^2/(ab))]` is equal to :
A
`0`

B
`1`

C
`2`

D
`abc`

Note: Not available
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Question: `(log_b a xx log_c b xx log_a c)` is equal to:
A
`0`

B
`1`

C
`abc`

D
`a + b + c`

Note: Not available
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Question: `[1/(log_xy (xyz)) + 1/((log_b ca) + 1) + 1/((log_zx (xyz))]` is equal to :
A
`1`

B
`2`

C
`3`

D
`4`

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`
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Question: `[1/((log_a bc) + 1) + 1/((log_b ca) + 1) + 1/((log_c ab) + 1) ]` is equal to :
A
`1`

B
`2`

C
`3`

D
`3/2`

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.`
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Question: If`log_2 [log_3 (log_2 x)] = 1,` then x is equal to :
A
`512`

B
`128`

C
`12`

D
`0`

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.`
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Question: `(log_5 3) (log_4 9) (log_3 2)` is equal to :
A
`2`

B
`1`

C
`5`

D
`3/2`

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`
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Question: If `log_10^2 = 0.3010` and `log_10^3 = 0.4771,` then the value of `log_10 1.5`is
A
`0.7161`

B
`0.1761`

C
`0.7116`

D
`0.7611`

Note: `log_10^(1.5)` `= log_10 (3/2)` `= log_10^3 - log_10^2` `= (0.4771 - 0.3010)` `= 0.1761.`
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Question: If `log_10^2 = 0.3010`, then `log_2 10` is :
A
`.3322`

B
`3.2320`

C
`3.3222`

D
`5`

Note: `log_2 10` ` = 1/(log_10 2)` `= 1/.3010` `= 10000/3010` `= 3.3222.`
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Question: The value of `log_2 (log_5 625)` is :

Question: The value of`(1/3 log_10 125 - 2log_10 4 + log_10 32)` is :

Question: `[log (a^2/(bc)) + log (b^2/(ac)) + log (c^2/(ab))]` is equal to :

Question: `(log_b a xx log_c b xx log_a c)` is equal to:

Question: `[1/(log_xy (xyz)) + 1/((log_b ca) + 1) + 1/((log_zx (xyz))]` is equal to :

Question: `[1/((log_a bc) + 1) + 1/((log_b ca) + 1) + 1/((log_c ab) + 1) ]` is equal to :

Question: If`log_2 [log_3 (log_2 x)] = 1,` then x is equal to :

Question: `(log_5 3) (log_4 9) (log_3 2)` is equal to :

Question: If `log_10^2 = 0.3010` and `log_10^3 = 0.4771,` then the value of `log_10 1.5`is

Question: If `log_10^2 = 0.3010`, then `log_2 10` is :