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Logarithm problems

1.
Find the value of log ₃₂2 ⁸ + log ₂₄₃3 ⁷ - log ₃₆1296?
Options
A. 3
B. 2
C. 1
D. 0

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2. If log72 = m, then log4928 is equal to ?
Options
A. 1/(1+2m)
B. (1+2m)/2
C. 2m/(2m+1)
D. (2m+1)/2m

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

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

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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.

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

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

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