Logarithms, General Mathematics

Question: The value of log``343`` 7 is :
A
`1/3`

B
`- 3`

C
`- 1/3`

D
`3`

Note: Let `long_343 7 = m.` Then, `(343)^m` `= 7 ⇒ (7^3)^m` `= 7 ⇔ 7^3m` `= 7^1 ⇔ 3m` `= 1 ⇔ m` `= 1/3`. `:. long_343 7 = 1/3.`
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Question: The value of log`5` (1/125) is :
A
`3`

B
`- 3`

C
`1/3`

D
`- 1/3`

Note: Let log`5 (1/125) = m` Then,`5m = 1/125 ⇔ 5^m` `= 1/5^3 ⇔ 5^m` `= 5-3` `:. m = - 3` and log`5(1/125)` `= -3`
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Question: The value of log`√2^32` is :
A
`5/2`

B
`5`

C
`10`

D
`1/10`

Note: Let log`√2 ^32` = m. Then,`(√2)^m = 32 ⇔ 2^m/2` `= 2^5 ⇔ m/2` `= 5 ⇔ m` `= 10` :.` log√2 ^32` `= 10`
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Question: The value of `log_10 (.0001)` is :
A
`1/4`

B
`-1/4`

C
`-4`

D
`4`

Note: Let `log_10 (.0001) = m`.Then, `10^m = .0001 ⇔ 10^m` `= 1/10000 ⇔ 10^m` `= 1/10^4 ⇔ 10^m` `= 10 ^-4 ⇔ m` `- 4`
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Question: The value of log`_(.01) (1000) is :`
A
`1/3`

B
`-1/3`

C
`3/2`

D
`- 3/2`

Note: Let log`_(.01) (1000) =m.` Then,`(.01)^m = 100 ⇔ (1/100)^m` `= 100` `⇔ (1/10^2)^m` `= 10^3 ⇔ (10 ^-2)^m` `= 10^3 ⇔ 10^-2m` `= 10^3.` `:. - 2m = 3 or m` `= - 3/2`
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Question: If `log_3 x = -2,` then x is equal to :
A
`- 9`

B
`- 6`

C
`- 8`

D
`1/9`

Note: `log_3 x = - 2 ⇔ x` `= 3 _2` `= 1/3^2` `= 1/9.`
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Question: If `log_x (9/16) = - 1/2,` then x is equal to :
A
`3/4`

B
`- 3/4`

C
`81/256`

D
`256/81`

Note: `log_x (9/16)` `= - 1/2 ⇔ x^- 1/2` `= 9/16 ⇔ 1/√x` `= 9/16 ⇔ √x` `= 16/9` :. x`= (16/9 xx 16/9)` `= 256/81.`
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Question: If `log_(10000^x) = - 1/4,` then, x is equal to :
A
`1/10`

B
`1/100`

C
`1/1000`

D
`1/10000`

Note: Not available
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Question: If `log_x 4 = 1/4,` then x is equal to :
A
`16`

B
`64`

C
`128`

D
`256`

Note: Not available
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Question: If`log_x (0.1) = - 1/3,` then the value of x is :
A
`10`

B
`100`

C
`1000`

D
`1/1000`

Note: `log_x (0.1) = - 1/3 ⇔ x^- 1/3` `= 0.1 ⇔ 1/(x^1/3)` `= 0.1` `:. x^1/3` `= 1/0.1` `= 10 or x = (10)^3` `= 1000.`
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Question: The value of log``343`` 7 is :

Question: The value of log`5` (1/125) is :

Question: The value of log`√2^32` is :

Question: The value of `log_10 (.0001)` is :

Question: The value of log`_(.01) (1000) is :`

Question: If `log_3 x = -2,` then x is equal to :

Question: If `log_x (9/16) = - 1/2,` then x is equal to :

Question: If `log_(10000^x) = - 1/4,` then, x is equal to :

Question: If `log_x 4 = 1/4,` then x is equal to :

Question: If`log_x (0.1) = - 1/3,` then the value of x is :