Aptitude Logarithm Test Paper 1

Answer: C

Explanation:

Let log_2√2 [1/256] = x

We know that log_a y = x is similar to a^x = y

So, we can write it as [1/256] = (2√2) ^x

Or, (2√2) ^x = [1/2⁸]

Or, [2¹ * 2^1/2]^x = 1/2⁸

Or, 2^3x/2 = 2-8

Therefore, 3x/2 = -8

Hence, x = (-8 * 2)/ 3 = -16/3

Answer: D

Explanation:

ATQ, log_a [1/36] = -2/3

We know that log_a y = x is similar to a^x = y

So, a ^(-2/3) = 1/36

Or, a ^(-2/3) = 1/6²

Or, a ^(-2/3) = 6^-2

Now, multiply and divide by 3 in the power of 6 to make the power equals to power of a.

So, a ^(-2/3) = 6^3(-2/3)

On comparing both side, we get a = 6³

Therefore, a = 216

Answer: D

Explanation:

ATQ, Log₄ (log₈ 64) = log₅ x...... (i)

Let, log₈ 64 = a

Or, 64 = 8^a, or 8^a = 8²

That means a=2

Now, put log₈ 64 = 2in equation 1.

Log₄ (2) = log₅ x...... (ii)

Now, let log₄ 2 = s

Or, 4^s = 2, or 2^2S = 2

Now, on comparing both side we get 2_s = 1, or s = ½

Put the value of s in equation 2

So, log₅ x = ½

Therefore, x = 5^1/2 = √5

Answer: A

Explanation:

Here, a² + b² = 7ab

Add both sides 2ab to make a formula.

Or, a² + b² + 2ab = 7ab + 2ab

Or, (a+b) ² = 9ab

Or, (a+b) ² / 9 = ab

Or, [1/3 (a+b)]² = ab

Now, taking log both sides

Therefore, log [1/3 (a+b)]² = log ab

We know that log m*n = log m + log n, and log mⁿ = n log m

So, 2 log [1/3 (a+b)] = log a + log b

Therefore, log [1/3 (a+b)] = 1/2(log a + log b)

= a² + b²

= 7ab

Answer: A

Explanation:

(log₃ x)(log_x 2x)(log_2x y) = log_x x²
We know that logb a =
Now, A =

B =

C =

Now, ATQ, A* B * C = log_x x²
Or, ** =

We know that, log_a mⁿ = n log_a m
=

We know that log_a a = 1
That means, log₃ y = 2
We know thatlog_a y = x is similar to a^x = y
Therefore, y = 3² = 9