Logarithms, General Mathematics

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`
1. Report
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`
1. Report
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.`
1. Report
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.`
1. Report
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`.
1. Report
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.`
1. Report
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.`
1. Report
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.`
1. Report
Question: If log x + log y = log (x + y), then :
A
`x = y`

B
`xy = 1`

C
`y = (x - 1)/x`

D
`y = x/(x - 1)`

Note: `log x + log y` `= log (x + y) ⇒ log (x + y)` `= log (xy)` `:. x + y = xy` `or y(x - 1)` `= x or y = x/(x - 1)`
1. Report
Question: If` log_10 125 + log_10 8 = x,` then x is equal to :
A
`3`

B
`- 3`

C
`1/3`

D
`.064`

Note: `log_10 125 + log_10 8` `= x ⇒ log_10 (125 xx 8) = x.` `:. x = log_10 (1000)` `= log_10 (10^3)` `= 3 log_10 10` `= (3 xx 1) = 3`
1. Report

First Prev 2 3 4 5 Next Last

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 :

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

Question: If log x + log y = log (x + y), then :

Question: If` log_10 125 + log_10 8 = x,` then x is equal to :