Which of the following statements is not correct?
log10 10 = 1
log (2 + 3) = log (2 x 3)
log10 1 = 0
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Answer : Option B
Explanation :
a) Since loga a = 1, so log10 10 = 1.
(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
log (2 + 3) log (2 x 3)(
(c) Since loga 1 = 0, so log10 1 = 0.
(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
2.870
2.967
3.876
3.912
Answer : Option C
=log29log(10/2)
=9log2log10−log2
=(9∗0.301001−0.3010
=2.7090.699
=2.709699
= 3.876
log√8log8is equal to:
1√8
14
18
log√8log8=log(8)1/2log8= €‹€‹12log8log8=12
If log 27 = 1.431, then the value of log 9 is:
0.934
0.945
0.954
0.958
log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
If logab+logba=log (a + b), then
a + b = 1
a - b = 1
a = b
a2 - b2 = 1
Answer : Option A
logab+logba=log (a + b)
log (a + b) = log[ab×ba]=log1
So, a + b = 1.
If log10 7 = a, then log10[170]is equal to:
- (1 + a)
(1 + a)-1
a10
110a
log1 [170]= log10 1 - log10 70
If log10 2 = 0.3010, then log2 10 is equal to:
699301
1000301
0.3010
0.6990
log2 10 =1log102=10.3010=100003010=1000301
If log10 2 = 0.3010, the value of log10 80 is:
1.6020
1.9030
3.9030
None of these
If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
1
3
5
10
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
log10 [5 (5x + 1)] = log10 [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9
x = 3.
The value of[1log360+€‹€‹[1log460+€‹€‹[1log560]is
0
60
If log 2 = 0.30103, the number of digits in 264 is:
19
20
21
Its characteristic is 19.
Hence, then number of digits in 264 is 20.
If logx[916]=−[12],then x is equal to:
−34
34
81256
25681
Answer : Option D
If logx[916]=−[12]
X−1/2=916
1√X=916
√X=169
x =[169]2
x =25681
If ax = by, then:
logab=XY
logalogb=XY
logalogb=YX
ax = by
log ax = log by
x log a = y log b
If logx y = 100 and log2 x = 10, then the value of y is:
210
2100
21000
210000
log 2 x = 10 x = 210.
logx y = 100
y = x100
y = (210)100 [put value of x]
y = 21000.
The value of log2 16 is:
4
8
16
Let log2 16 = n.
Then, 2n = 16 = 24 n = 4.
log2 16 = 4.
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log (2 + 3) 
log (2 x 3)(
log (33 ) = 1.431