Logarithm- Aptitude Questions and Answers - in Hindi

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if log 3 = 0.477 and (1000)^x = 3, then x equals to ?

A) 0.159
B) 10
C) 0.0477
D) 0.0159

Correct Answer :
0.159

Explanation :

log_a(x^p)=p(log_ax)
log_x x=1

(1000)^x = 3
⇒ log₁₀10^3x = log₁₀3
⇒ 3x = log₁₀3
⇒ x = log₁₀3 / 3 = 0.477 / 3 = 0.159

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The value of log₂3 x log₃2 x log₃4 x log₄3 is ?

A) 1
B) 2
C) 3
D) 4

Correct Answer :
1

Explanation :

log_ax = log_bx/log_ba=log x/log a

Thus, log₂3 x log₃2 x log₃4 x log₄3
=> (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)
=> 1

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The value of log 9/8 - log 27/32 + log3/4 is ?

A) 0
B) 1
C) 2
D) 3

Correct Answer :
0

Explanation :

log_a(xy) = log_a x + log_a y
log_a (x/y) = log_a x - log_a y
log_a 1 = 0

Thus, log 9/8 - log 27/32 + log3/4 => log [(9/8) /(27/32)] + log3/4
=> log 4/3+ log3/4
=> log [(4/3)*(3/4)]
=> log 1
=> 0

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The equation log_ax + log_a (1+x)=0 can be written as ?

A) x² + x - 1 = 0
B) x² + x + 1 = 0
C) x² + x - e = 0
D) x² + x + e = 0

Correct Answer :
x² + x - 1 = 0

Explanation :

log_a(xy) = log_a x + log_a y
log_a 1 = 0

So, log_ax + log_a(1+x) = 0
⇒ log_ax (x+1) = log_a1
⇒ x(x +1) = 1
⇒ x² + x - 1 = 0

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Find the value of log₉ 81 - log₄ 32 ?

A) 1 / 2
B) - 3 / 2
C) - 1 / 2
D) 2

Correct Answer :
- 1 / 2

Explanation :

log_ax = log_bx/log_ba=log x/log a.
log_a(x^p)=p(log_ax)

log₉ 81 - log₄ 32
=> log₃² 3⁴ - log₂² 2⁵
=>(log 3⁴ / log 3²) - ( log 2⁵/ log2²)
=>(4 log 3 / 2 log 3) - ( 5 log 2 / 2 log2)
=> 4/2 - 5/2
=> -1/2

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log_-1/3 81 is equal to ?

A) - 27
B) - 4
C) 4
D) 127

Correct Answer :
- 4

Explanation :

log_x x=1

y=x^xis equivalent to, log_xy = log_xx ⇒ log_xy =x

Let, log_-1/381 = x
⇒ 81 = (-1/3)^x
⇒ 3⁴ = (-1/3)^x = 3^-x
⇒ x = -4

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The value of log₁₀ 0.000001 is ?

A) 6
B) - 6
C) 5
D) - 5

Correct Answer :
- 6

Explanation :

log₁₀ 10^-6 = -6

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The value of log₆ log₅ 15625 is ?

A) 1
B) 2
C) 3
D) 4

Correct Answer :
1

Explanation :

log₆ log₅15625 = log₆ log₅(5)⁶
= log₆6(log₅5) = 1

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If log₁₀₀₀₀x = -1/4, then x is ?

A) 1 / 100
B) 1 / 10
C) 1 / 20
D) 1

Correct Answer :
1 / 10

Explanation :

log₁₀⁴x = -1/4
⇒ x = (10⁴)^-1/4
= 1/10

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Given that log₁₀ 2 = 0.3010 the value of log₁₀ 5 is ?

A) 0.3241
B) 0.6911
C) 0.6990
D) 0.7525

Correct Answer :
0.6990

Explanation :

log₁₀5 = log₁₀(10/2)
= log₁₀10 - log₁₀2
= 1-0.3010
= 0.6990

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The value of log 128 - log 8 / log 4 is ?

log 128 - log 8 / log 4 का मान है?

Correct Answer :
2

Explanation :

log 128 - log 8 / log 4
=> log (128/8) / log 4
=> log 16 / log 4
=> log 4² / log 4
=> 2 log 4 / log 4
=> 2

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What is the solution of the equation xlog₁₀(10/3) + log₁₀3= log₁₀(2 + 3^x ) + x ?

समीकरण xlog₁₀(10/3) + log₁₀3= log₁₀(2 + 3^x ) + x का हल क्या है?

Correct Answer :
0

Explanation :

xlog₁₀(10/3) + log₁₀3= log₁₀(2 + 3^x ) + x
log₁₀(10/3)^x + log₁₀3= log₁₀(2 + 3^x ) + log₁₀10^x[ because log_aa =1, log a^m = m log a]
log₁₀(10/3)^x * 3= log₁₀(2 + 3^x ) * 10^x[ because log_ca + log_cb = log_cab ]
(10/3)^x * 3= (2 + 3^x ) * 10^x
3*10^x/3^x = (2 + 3^x ) * 10^x
3*10^x = 3^x* 10^x*(2 + 3^x )
3 = 3^x*(2 + 3^x )

Let 3^x = y Then 3 = y*(2 + y )
y²+ 2y - 3=0
( y + 3)( y - 1) = 0
y = -3, 1 that is 3^x = -3, 1

consider 3^x = 1 [3^x ≠ -3]
3^x = 1⁰
Hence x = 0

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