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Arithmetic Aptitude :: Logarithm

Home > Arithmetic Aptitude > Logarithm > General Questions

1. If log 125 + log 8 = x, then x is equal to

Answer: 3

Explanation:

log 125 + log 8 = log (125 * 8)
=> log (1000) = log (10^3)
=> 3 log 10 = 3

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2. If log5 + log(5x+1) = log(x+5) + 1, then x is equal to

Answer: 3

Explanation:

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3. If log 0.318=0.3364 and log 0.317=0.33320 then log 0.319 =?

Answer: 0.3396

Explanation:

log 0.319=log0.318+(log0.318-log0.317) = 0.3396

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4. If log 0.317=0.3332 and log 0.318=0.3364 then find log 0.319 ?

Answer: 0.3396

Explanation:

log 0.317=0.3332 and log 0.318=0.3364
then
log 0.319=log0.318+(log0.318-log0.317)
=0.3396

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5. If log(base 10) 5 + log(base 10)(5x + 1) = log(base 10)(x + 5) + 1, then x is equal to:

Answer: 3

Explanation:

Given log(base 10) 5 + log(base 10)(5x + 1) = log(base 10)(x + 5) + 1
=> log(base 10) 5 + log(base 10)(5x + 1) = log(base 10)(x + 5) + log(base 10) 10
Hint: log (base Z)Z = 1
=> log(base 10)[5 (5x + 1)] = log(base 10) [10(x + 5)] ------ (Point to Remember.)
=> 5(5x + 1) = 10(x + 5)
=> 5x + 1 = 2x + 10
=> x = 3

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6. When numbers are written in base b, we have 15*22 = 414, the value of b is

Answer: 6

Explanation:

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7. The Value of log8(64) - log64(4096) is

Answer: 0

Explanation:

log8 (64)-log64(4096)
log8 (8^2)-log 64(64^2) = 2 - 2 = 0

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8. log base 12 144p=3 then p= ?

Answer: 12

Explanation:

log base 12 144p=3
=> 144p=12^3
=> 144p=12^2 *12
=> 144p=144*12
=> p=12

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9. Change 101010two to base ten.

Answer: 42

Explanation:

(101010) base2 = (1*2^5 + 0*2^4 + 1*2^3 +0*2^2 + 1*2^1 + 0*2^0) 10 = (42) base10

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