Q.2. . If log 2 = 03.301 and log 3 = 0.4771, find the value of log3 72
5
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A. 19.46
B. 18.96
C. 21.54
D. 14.48
Q.3. If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of (1/log
x+zy) + (1/log
x-zy)
Sol : Option B
Here x, y and z are the sides of a right angled triangle, so z
2 = x
2 + y
2.
Q.4. Find the value of log
2 2 + log
2 2
2 + log
2 2
3 + ........ + log
2 2
n.
A. n(n+1)/2
B. n+1
C. n
D. 2n
Sol : Option A
log2 2 + log2 22 + log2 23 + ........ + log2 2n
log2 2 + 2log2 2 + 3log2 2 + ........ + nlog2 2
1+2+3+........+n
n(n+1)/2
Q.5. If log
5 16, log
5 (3
x-4), log
5 (3
x+97/16) are in arithmetic progression, then x is
Sol : Option B
log
5 16, log
5 (3
x-4), log
5 (3
x+97/16) are in arithmetic progression
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Q.6. If ‘x’ is an integer then solve (log
2 x)
2 – log
2 x
4 - 32 = 0.
A. 125
B. 256
C. 375
D. None of these
Sol : Option B
We have (log2 x) 2 – log2 x4 - 32 = 0.
⇒ (log2 x) 2 – 4log2 x - 32 = 0......(1)
Let log2 x = y
(i) ⇒ y2 – 4y – 32 = 0
⇒ y2 – 8y + 4y – 32 = 0
⇒ y (y – 8) + 4 (y – 8) = 0
⇒ (y – 8) (y + 4) = 0
⇒ y = 8, -4
⇒ log2 x = 8 or log2 x = - 4
⇒ x = 28 = 256 or x = 2-4 = 1/16
Since ‘x’ is an integer so x = 256.
Q.7. If log
5y – logsub>5√y = 2 log
y 5, then find the value of y.
Sol : Option A
We have log
5y – logsub>5√y = 2 log
y 5
Q8. If (1/4)log
2x + 4log
2y = 2 + log
64-18 then
A. y16 = 64/x2
B. x16 = 64/y
C. y16 = 8/x4
D. y16 = 64/x
Sol : Option D
We have (1/4)log
2x + 4log
2y = 2 + log
64-18
Q9. If log 2 = 0.301 and log 3 = 0.4771, find the number of digits in 48
12.
Sol : Option B
We have log 4812 = 12 × log 48 = 12 × log (24 × 3)
= 12 × (4 log 2 + log 3)
= 12 × (4 × 0.301 + 0.4771)
= 12 × (1.204 + 0.4771)
= 12 × 1.6811 = 20.1732
Now the characteristic is 20, so the number of digits = 20 + 1 = 21.
Q10. If log
3[log
2 (x
2 – 4x – 37)] = 1, where ‘x’ is a natural number, find the value of x.
Sol : Option A
We have log3[log2 (x2 – 4x – 37)] = 1
⇒ [log2 (x2 – 4x – 37)] = 3
⇒ x2 – 4x – 37 = 8
⇒ x2 – 4x – 45 = 0
⇒ (x – 9) (x + 5) = 0
⇒ x = 9, - 5
Since x is a natural number, so x = 9.