#### Data Interpretation

• ( 1 ) Evaluate: log9 27 - log27 9

• 1) 2-Mar
• 2) 6-May
• 3) 1
• 4) 3-Feb
• Discussion in forum
Solution : log9 27 - log27 9
=> (log 27/log 9) - (log 9/log 27)
=> (log 33/log 32) - (log 32/log 33)
=> (3log 3/2log 3) - (2log 3/3log 3)
=> (3/2) - (2/3) = 5/6

discussion

• ( 2 ) If log64 7 = x log4 7 then x = __________

• 1) 4
• 2) log464
• 3) 3-Jan
• 4) log43
• Discussion in forum
Solution : log64 7 = x log4 7
=> (log 7/log 64) = x (log 7/log 4)
=> (log 7/log 43) = x (log 7/log 4)
=> (log 7/3log 4)* (log 4/log 7) = x
=> x = 1/3

discussion

• ( 3 ) if ax = by, then

• 1) log a/log b = x/y
• 2) log a/b = x/y
• 3) log a/log b = y/x
• 4) None of these
• Discussion in forum
Answer : 3) log a/log b = y/x
Solution : ax = by
taking log both side
log ax = log by
=> xlog a = ylog b
=> log a/log b = y/x

discussion

Answer : 3) log a/log b = y/x

• ( 4 ) If logx (xy) = x, then logy (xy) is :

• 1) 1/a
• 2) a/(a+1)
• 3) a/(1-a)
• 4) a/(a-1)
• Discussion in forum
Solution : Given,
logx (xy) = a
=> log xy/log x = a
=> (log x + log y)/log x = a
=> (log x/log x) + (log y/log x) = a
=> 1 + (log y/log x) = a
=> (log y/log x) = a - 1.................(1)
logy (xy)
=> log xy/log y
=> (log x + log y)/log y
=> (log x/log y) + (log y/log y)
=> (1/a -1) + 1 (from equation (1)]
=> (1 + a - 1)/(a - 1)
=> a/(a - 1)

discussion

• ( 5 ) if log 2 = 0.30103, then the value of log2 10 is:

• 1) 699/301
• 2) 1000/301
• 3) 0.301
• 4) 0.699
• Discussion in forum
Solution : log2 10 = 1/log10 2 = 1/0.3010 = 10000/3010 = 1000/301.

discussion

• ( 6 ) If log10 125 + log10 8 = x, then x is equal to:

• 1) 3
• 2) -3
• 3) 3-Jan
• 4) 0.064
• Discussion in forum
Solution : log10 125 + log10 8 = x
=> log10 (125*8) = x
=> log10 1000 = x
=> log10 103 = x
=> 3log1010 = x
=> x = 3.

discussion

• ( 7 ) Evaluate: log100 (0.01)

• 1) 1
• 2) 0
• 3) -1
• 4) -2
• Discussion in forum
Solution : Let log100 (0.01) = n
Then, (100)n = 0.01 = 1/100 = (100)-1
so, n = -1
log100 (0.01) = -1

discussion

• ( 8 ) The value of log5 (1/125) is :

• 1) 3
• 2) -2
• 3) -3
• 4) 2
• Discussion in forum
Solution : Let log5 (1/125) = x
Then, 5x = (1/125) = (1/53) = 5-3
x = - 3

discussion

• ( 9 ) logx(9/32) = -1/8, find the value of x

• 1) (9/32)8
• 2) (9/32)2
• 3) (32/9)8
• 4) (32/9)2
• Discussion in forum
Solution : logx(9/32) = ?1/8
=> x-1/8 = 9/32
=> 1/x1/8 = 9/32
=> x1/8 = 32/9
=> x = (32/9)8

discussion

• ( 10 ) If log(a/b) + log(b/a) = log(a+b), then

• 1) a = b
• 2) a + b = 1
• 3) a - b = 1
• 4) a2 - b2 = 1
• Discussion in forum
Answer : 2) a + b = 1
Solution : log(a/b) + log(b/a) = log(a + b)
=> log [(a/b) * (b/a)] = log(a + b)
=> log(1)=log(a + b)
=> a + b = 1

discussion

Answer : 2) a + b = 1