Aptitude Logarithm Test Paper 2

Answer: A

Explanation:

x =1 + log_a bc

We can write it as x = log_a a + log_a bc => log_a abc

Similarly, y = log_b b + log_b ca => log_b abc

And, z = log_c c + log_c ab => log_c abc
Changing the values of x, y, z to a common base m by using log_b a =, we get
X =

Y =

Z =

Now, =[log_m a + log_m b + log_m c]

Now, Right hand side equation, [log_m abc/ log_m abc] = 1
Now, = 1

Or, = 1 => xyz =xy + yz + zx.

Answer: B

Explanation:

i) The number 5631> 1 and the number of digits in the integral part are 4.
Therefore, the characteristics of the logarithm are 4-1 = 3,

ii) In the number 5.678, the number of digits in the integral part = 1.
Therefore, characteristics of the logarithm are 1-1 =0

iii) In this case, the number of digits in an integral part of the number 56.23 are 2.
Therefore, the characteristics of the logarithm = 2-1 = 1

So, the option b is correct.

Answer: C

Explanation:

We have to take 6²⁰ with log
We know that log mⁿ = n log m
Now, log 6²⁰ = 20 log 6
Or, 20 log (2*3)
We know that log (m*n) = log m + log n
Now, 20 [log 2 + log 3] = 20 [0.30103 + 0.47712] = 20 [0.77815]
Since, the number of digits in 6²⁰ = 15.563, round up value = 16
Therefore the number of digits = 16

Answer: A

Explanation:

Let Log_0.001 (0.0001) = x

We know that log_x y = a equals to x^a = y.

So, (0.001)^x= 0.0001
Or, = [1/10000]

Or, =

Therefore, compare both side, we get 3x = 4.

Hence, x = 4/3

Answer: C

Explanation:

Here log_b x = ͞5.1342618 is given and log₁₀(x^(1/4)) is asked

That means here b also treat as base 10

Now, we can say log₁₀ x = ͞5.1342618 = -5 + 0.1342618 => -4.8657382

Therefore, log₁₀ (x^1/4) = ¼ log₁₀ x

Or, ¼ (-4.8657382) = -1.21643455, but it is not in the option.

To make it -2, we have to subtract 0.7835655 from -1.21643455

i.e., -1.21643455 - 0.7835655 = -2

Now, to get back on the original value we have to add 0.7835655 in -2.

Or, -2 + 0.7835655 = ͞2.7835655

Hence, the c is correct.