CRE 1 - Logarithms | Algebra - Logarithms
If = 5, find the value of a.
- A.
27
- B.
243
- C.
9
- D.
81
Answer: Option B
Explanation :
Given, =5
∴ 35 = a
⇒ a = 243.
Hence, option (b).
Workspace:
Find the value of
- A.
- B.
-3
- C.
-2
- D.
Answer: Option C
Explanation :
Given,
= -2.
Hence, option (c).
Workspace:
log〖343√7〗 to the base 7 is equal to
- A.
3
- B.
3/2
- C.
7/2
- D.
None of these
Answer: Option C
Explanation :
Hence, option (c).
Workspace:
Answer: 125
Explanation :
Given,
⇒ x = 125
Hence, 125
Workspace:
If , then find the value of x
- A.
- B.
- C.
343
- D.
49
Answer: Option D
Explanation :
Given,
we know,
Hence, option (d).
Workspace:
Find the value of
- A.
1
- B.
2
- C.
3
- D.
4
Answer: Option B
Explanation :
Given ,
Hence, option (b).
Workspace:
Find the value of .
- A.
10/2
- B.
10
- C.
2
- D.
log 30
Answer: Option D
Explanation :
We know
Given,
Converting all logs in base 10, we get:
=
Hence, option (d).
Workspace:
Find the value
- A.
0
- B.
1
- C.
3
- D.
log(3/4)
Answer: Option A
Explanation :
Given = log 16 – log 27 – (log 64 - log 81) + log 4 – log3
= 2log4 – 3log3 – 3log4 + 4log3 + log4 – log3 = 0
Alternately,
=
= log 1 = 0
Hence, option (a).
Workspace:
Evaluate
- A.
192
- B.
64
- C.
64/3
- D.
Answer: Option C
Explanation :
Given :
Hence, option (c).
If log2 [log3 (log2x)]=0, then x is equal to
Solution:
Hence , 8
Workspace:
The value of is equal to
Answer: 2
Explanation :
We know , and
Hence , 2.
Workspace:
If then x is
- A.
243
- B.
729
- C.
- D.
625
Answer: Option C
Explanation :
Hence, option (c).
Workspace:
The value of is
- A.
log3
- B.
log5
- C.
log7
- D.
log2
Answer: Option D
Explanation :
Given,
= log2
Hence, option (d).
Workspace:
If ,then the value of a is
- A.
bc
- B.
c/b
- C.
- D.
Answer: Option C
Explanation :
Given
Hence, option (c).
Workspace:
If , then find the value of y.
- A.
1
- B.
2
- C.
3
- D.
5
Answer: Option D
Explanation :
Given, logx = 8
=> y8 = x
Dividing (2) by (1)
⇒y=5
Hence, option (d).
Workspace:
log 0.0867=?
- A.
log 8.67 +2
- B.
log 8.67 - 2
- C.
- D.
-2log 8.67
Answer: Option B
Explanation :
Given, log 0.0867
= log (8.67/ 100)
= log 8.67 – log 100
= log 8.67 – 2
Hence, option (b).
Workspace:
Find x, if 0.01x = 2
- A.
log 2/2
- B.
2/log2
- C.
-2/ log2
- D.
-log 2/2
Answer: Option D
Explanation :
Given, 0.01x = 2.
⇒x=
Hence, option (d).
Workspace:
If , , then the value of 𝑥 is (log 2 = 0.3010, log 3 = 0.4771)
- A.
2.3
- B.
1.59
- C.
1.8
- D.
1.41
Answer: Option B
Explanation :
Given,
⇒x(0.3010 + 2 × 0.4771) = 2
Hence, option (b).
Workspace:
If log 2 = 0.30103, find the number of digits in 260
- A.
19
- B.
31
- C.
100
- D.
200
Answer: Option A
Explanation :
Number of digits in Na is one more than the characteristic of log10Na.
∴ log(260) = 60 log 2 = (60×0.30103)=18.06.
⇒ Its characteristic is 18.
Hence, the number of digits in 260 is 19.
Hence, option (a).
Workspace:
The mantissa of log 3274 is 0.5150. The value of log (0.3274) is
- A.
1.5150
- B.
1.5150
- C.
2.5150
- D.
None of these
Answer: Option A
Explanation :
Since, 0.3274 gives characteristic 1 ̅.
Therefore, value of log (0.3274) = 1 ̅.5150
Hence, option (a).
Workspace:
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