If a2+b2 = c2 , then 1logc+ab + 1logc-ab = ? 1 2 4 8 Given a 2 + b 2 = c 2 Now 1

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Question
If a2+b2 = c2 , then 1logc+ab + 1logc-ab = ?
Options
A. 1
B. 2
C. 4
D. 8

Correct Answer

2

Explanation

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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

Discuss

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.

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

Discuss

Correct Answer: 3/2

Explanation:

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

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

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

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

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

Discuss

5. if log105+log5x+1=log10(x+5)+1,then x is equal to
Options
A. 1
B. 3
C. 5
D. 10

Discuss

7. Which of the following statements is not correct?
Options
A. log10 = 1
B. log (2 + 3) = log (2 x 3)
C. log1 = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3

Discuss

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

Discuss

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If a2+b2 = c2 , then 1logc+ab + 1logc-ab = ?

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If a2+b2 = c2 , then 1logc+ab + 1logc-ab = ?

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