General Mathematics

Question: The value of`(1/(log_3 60) + 1/(log_4 60) + 1/log_5 60)`is
A
`0`

B
`1`

C
`5`

D
`60`

Note: Given Expression `= log_60 3 + log_60 4 + log_60 5` `= log_60 (3 xx 4 xx 5)` `= log_60 60` `= 1`
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Question: The value of`(log_3 4) (log_4 5) (log_5 6) (log_6 7) (log_7 8) (log_8 9)`
A
`2`

B
`7`

C
`8`

D
`33`

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`
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Question: If`log_10 2 = 0.30103,`the value of `log_10 5` is :
A
`0.3241`

B
`0.6911`

C
`0.6990`

D
`0.7525`

Note: `log_10 5 = log_10 (10/2)` `= log_10 10 - log_10 2` `= 1 - log_10 2` `= (1 - 0.3010)` `= 0.6990`.
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Question: If`log_10 2 = 0.30103`, the value of `log_10 50` is :
A
`.69897`

B
`1.30103`

C
`1.69897`

D
`2.30103`

Note: `log_10 50` `= log_10 (100/2)` `= log_10 100 - log_10 2` `= 2 - 0.30103` `= 1.69897`
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Question: If`log_10 2 = 0.3010`, the value of `log_10 80`is :
A
`1.9030`

B
`1.6020`

C
`3.9030`

D
None of these

Note: `log_10 80` `= log_10 (8 xx 10)` `= log_10 8 + log_10 10` `= log_10 2^3 + 1` `= (3 log_10 2) + 1` `= (3 xx 0.3010) + 1` `= 1.9030`
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Question: If`log_10 2 = 0.3010,` the value of `log_10 25` is :
A
`1.5050`

B
`1.3980`

C
`1.2040`

D
`0.6020`

Note: `log_10 25` `= log_10 (100/4)` `= log_10 100 - log_10 4` `= 2 - 2 log_10 2` `= (2 - 2 xx 0.3010)` `= (2 - 0.6020)` `= 1.3980.`
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Question: The value of`(log_9 27 + log_8 32)` is :
A
`4`

B
`7`

C
`7/2`

D
19/6`

Note: `let `log_9 27 = x.` Then,`9^x = 27 ⇔ (3^2)^x` `= 3^3` `:. 3^2x = 3^3.` `So, 2x = 3` `or x = 3/2.` let`log_8 32 = y.` Then, `8^y = 32` `or (2^3)^y = 2^5.` `:.2^3y = 2^5.` So,`3y = 5` `or y = 5/3`. `:. log_9 27 + log_8 32` `= (3/2 + 5/3)` `= 19/6.`
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Question: `If`log_4 x + log_2 x = 6,` then the value of x is :
A
`2`

B
`4`

C
`8`

D
`16`

Note: Given equation is `(log x)/(log 4) + (log x)/(log 2) = 6` `or (log x)/(2 log 2) + (log x)/(log 2) = 6` `or 3 log x = 12 log 2.` `:. log x = 4 log 2` `= log 2^4.` `So, x = 16`.
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Question: If `log_10 (0.1) = -1,`then`log_10 (.001)` is :
A
`- 1.3`

B
`- 2`

C
`- 2.3`

D
`-3`

Note: `log_10 (.001)` `= log_10 (.1/100)` `= log_10 (.1) - log_10 (100)` `= (- 1 - 2)` `= -3.`
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Question: If`log_5 (x^2 + x) - log_5 (x + 1) = 2,` then the value of x is :
A
`5`

B
`32`

C
`25`

D
`10`

Note: `log_5 (x^2 + x) - log_5 (x + 1)` `= 2 ⇒ log_5 ((x^2 + x)/(x + 1))` `= 2` `:.log_5 [ (x (x + 1)/(x + 1)]` `= 2 or log_5 x` `= 2 or x = 5^2` `= 25.`
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Question: The value of`(1/(log_3 60) + 1/(log_4 60) + 1/log_5 60)`is

Question: The value of`(log_3 4) (log_4 5) (log_5 6) (log_6 7) (log_7 8) (log_8 9)`

Question: If`log_10 2 = 0.30103,`the value of `log_10 5` is :

Question: If`log_10 2 = 0.30103`, the value of `log_10 50` is :

Question: If`log_10 2 = 0.3010`, the value of `log_10 80`is :

Question: If`log_10 2 = 0.3010,` the value of `log_10 25` is :

Question: The value of`(log_9 27 + log_8 32)` is :

Question: `If`log_4 x + log_2 x = 6,` then the value of x is :

Question: If `log_10 (0.1) = -1,`then`log_10 (.001)` is :

Question: If`log_5 (x^2 + x) - log_5 (x + 1) = 2,` then the value of x is :