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Aptitude Logarithm Test Paper 3


11) The value of Log10 2 + 16 log10 Apti Logarithm+ 12 log10 Apti Logarithm+ 7 log10 Apti Logarithm is

  1. 3
  2. 2
  3. 1
  4. 0

Answer: C

Explanation:
Log10 2 + 16 log10 Apti Logarithm+ 12 log10 Apti Logarithm+ 7 log10 Apti Logarithm

We know that log mn = n log m

So, Log10 2 + log10 [24/ 3*5] 16 + log10 [52/ 23 * 3] 12 + log10 [34/ 24 * 5] 7

Or, log10 2 + log10 [264/ 316 * 516] + log10 [536/ 236 * 312] + log10 [328/ 228 * 57]

We know that log m*n = log m + log n

Now, log10 [2 * 264 * 524 * 328]/ [316 * 516 * 236 * 312 * 228 * 57]

Or, log10 [265 * 328 *524]/ [264 * 328 *523]

Therefore, log10 (2*5) = log10 (10) = 1


12) If Apti Logarithmlog (11 + 4√7) = log (2 + x), what is the value of x?

  1. √7
  2. 11
  3. 4
  4. 2

Answer: A

Explanation:

We have Apti Logarithmlog (11 + 4√7) = log (2 + x)

Now, we can write it as Apti Logarithmlog (7 + 4 + 4√7) = log (2 + x)

We know that (a+b) 2 = a2 + b2 + 2ab

Similarly, Apti Logarithmlog (2 + √7) 2 = log(2 + x)

Or, Apti Logarithmlog (2 +√7) = log (2 + x)

Both side Log will be canceled out

Now, 2 + √7 = 2 + x

Therefore, x = 2 + √7 - 2 = √7


13) If log10 Apti Logarithm = 2, find the value of x.

  1. 2, 10
  2. 1, 5
  3. 12, 24
  4. 6, 30

Answer: A

Explanation:

We have log10 Apti Logarithm = 2

Or, we can write it as log10 Apti Logarithm = 2 log10 10

Or, log10 Apti Logarithm = 2 log10 100

Therefore, both side log will be canceled out.

Apti Logarithm

Or, Apti Logarithm = 4

We know that √x = a, or x1/2 = a, then x = a2

Similarly, x2 - 12x + 36 = 42

Or, x2 - 12x + 36 = 16

Or, x2 - 12x + 20=0

Now, (x-2)(x-10) = 0

Or, x-2 = 0, and x-10 =0

Therefore, we can say that x = 2, x = 10


14) If f(a) = log Apti Logarithm, f (2a / 1+a2) is equals to

  1. 0
  2. 1
  3. 2f(a)
  4. None of these

Answer: C

Explanation:
We have an expression f(a) = log Apti Logarithm, then we have to find the value of f(2a / 1+a2).

We can find it by replacing a with Apti Logarithm

Now, fApti Logarithm= log Apti Logarithm

Or, log Apti Logarithm

Now, the denominator of both fractions will cancel out each other.
Now, fApti Logarithm= log Apti Logarithm

Or, log Apti Logarithm = log Apti Logarithm

We know that log mn = n log m.
Therefore, 2 log Apti Logarithmis equals to 2 f(a).


15) The value of log10Apti Logarithmis

  1. 4
  2. 3
  3. 2
  4. 1

Answer: D

Explanation:
We know that, if a number is in the form Apti Logarithm

Then the output will be the number itself, i.e., the expressionApti Logarithmis equals to 10.

Since, logm m = 1

Therefore, log10 (10) = 1


Aptitude Logarithm Test Paper 1
Aptitude Logarithm Test Paper 2
Aptitude Logarithm Test Paper 4





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