if logab+logba=loga+b,then a + b = 1 a - b = 1 a = b ab=1 i f log a b + log b a

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Correct Answer

a + b = 1

Explanation

$i f \log \frac{a}{b} + \log \frac{b}{a} = \log (a + b), t h e n$

$\log (a + b) = \log (\frac{a}{b} � \frac{b}{a}) = \log 1$

so, a+b=1

Logarithm problems

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2. A fast moving superfast express crosses another pasenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also the length of faster ntrain is 100m, then find the length of the slower train if they are moving in the same direction.
Options
A. 100 m
B. 125 m
C. 150 m
D. 175 m

Discuss

3. If log 64 = 1.8061, then the value of log 16 will be (approx)?
Options
A. 1.9048
B. 1.2040
C. 0.9840
D. 1.4521

Discuss

5. Find the logarithm of 144 to the base 23 :
Options
A. 2
B. 4
C. 8
D. None of these

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

Discuss

8. 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:

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

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

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

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

9. 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.

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if logab+logba=loga+b,then

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if logab+logba=loga+b,then

Logarithm problems

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