The Value of logtan10+logtan20+??+logtan890 is -1 0 1/2 1 = log tan 1 0 + log ta

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Question
The Value of logtan10+logtan20+??+logtan890 is
Options
A. -1
B. 0
C. 1/2
D. 1

Correct Answer

0

Explanation

$= [\log \tan (1^{0}) + \log \tan (89^{0})] + [\log \tan (2^{0}) + \log \tan (88^{0})] + ? ? + [\log \tan (45^{0})]$

$= \log [\tan (1^{0}) � \tan (89^{0})] + \log [\tan (2^{0}) � \tan (88^{0})] + ? ? + \log (1)$

$[? \tan (90 - ?) = c o t ? a n d \tan (45^{0}) = 1]$

= log 1 + log 1 +.....+log 1

= 0.

Logarithm problems

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1. Find value of log27 +log 8 +log1000log 120
Options
A. 1/2
B. 3/2
C. 2
D. 2/3

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Correct Answer: 3/2

Explanation:

$= \frac{\log \sqrt{3^{3}} + \log 2^{3} + \log \sqrt{10^{3}}}{\log (10 � 3 � 2^{2})}$

$= \frac{\log (3^{3})^{\frac{1}{2}} + \log 2^{3} + \log {(10^{3})}^{\frac{1}{2}}}{\log (10 � 3 � 2^{2})}$

$= \frac{\frac{1}{2} \log 3^{3} + 3 \log 2 + \frac{1}{2} \log 10^{3}}{\log 10 + \log 3 + \log 2^{2}}$

$= \frac{\frac{3}{2} (\log 3 + 2 \log 2 + \log 10)}{\log 3 + 2 \log 2 + \log 10}$ = $\frac{3}{2}$

2. What is the characteristic of the logarithm of 0.0000134?
Options
A. 5
B. -5
C. 6
D. -6

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3. For x?N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?
Options
A. p < q
B. p = q
C. p > q
D. can't be determined

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8. Find x if log1218 = log24x + 1. log24x+1 + 4
Options
A. 0
B. 1
C. 2
D. None of these

Discuss

9. The value of x satisfying the following relation: log12x = log23x-2
Options
A. 1/3
B. -1/3
C. 3
D. None of these

Discuss

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The Value of logtan10+logtan20+??+logtan890 is

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The Value of logtan10+logtan20+??+logtan890 is

Logarithm problems

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