# Logarithm- Aptitude Questions and Answers

 The value of log23 x log 32 x log34 x log43 is ? 1 2 3 4 Correct Answer :1 Explanation :logax = logb x/logb a=log x/log a Thus, log23 x log 32 x log34 x log43 => (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) => 1 The value of log 9/8 - log 27/32 + log3/4 is ? 0 1 2 3 Correct Answer :0 Explanation :loga(xy) = loga x + loga y loga (x/y) = loga x - loga y loga 1 = 0 Thus, log 9/8 - log 27/32 + log3/4 => log [(9/8) /(27/32)] + log3/4 => log 4/3+ log3/4 => log [(4/3)*(3/4)] => log 1 => 0 The equation logax + loga (1+x)=0 can be written as ? x2 + x - 1 = 0 x2 + x + 1 = 0 x2 + x - e = 0 x2 + x + e = 0 Correct Answer :x2 + x - 1 = 0 Explanation :loga(xy) = loga x + loga y loga 1 = 0 So, logax + loga(1+x) = 0 ⇒ logax (x+1) = loga1 ⇒ x(x +1) = 1 ⇒ x2 + x - 1 = 0 if log 3 = 0.477 and (1000)x = 3, then x equals to ? 0.159 10 0.0477 0.0159 Correct Answer :0.159 Explanation :loga(xp)=p(logax) logx x=1 (1000)x = 3 ⇒ log10103x = log103 ⇒ 3x = log103 ⇒ x = log103 / 3 = 0.477 / 3 = 0.159 Find the value of log9 81 - log4 32 ? 1 / 2 - 3 / 2 - 1 / 2 2 Correct Answer :- 1 / 2 Explanation :logax = logb x/logb a=log x/log a. loga(xp)=p(logax) log9 81 - log4 32 => log32 34 - log22 25 =>(log 34 / log 32) - ( log 25/ log22) =>(4 log 3 / 2 log 3) - ( 5 log 2 / 2 log2) => 4/2 - 5/2 => -1/2 log-1/3 81 is equal to ? - 27 - 4 4 127 Correct Answer :- 4 Explanation :logx x=1 y=xx is equivalent to, logxy = logxx ⇒ logxy =x Let, log-1/381 = x ⇒ 81 = (-1/3)x ⇒ 34 = (-1/3)x = 3-x ⇒ x = -4 The value of log10 0.000001 is ? 6 - 6 5 - 5 Correct Answer :- 6 Explanation : log10 10-6 = -6 The value of log6 log5 15625 is ? 1 2 3 4 Correct Answer :1 Explanation :log6 log515625 = log6 log5(5)6 = log66(log55) = 1 If log10000x = -1/4, then x is ? 1 / 100 1 / 10 1 / 20 1 Correct Answer :1 / 10 Explanation :log104x = -1/4 ⇒ x = (104)-1/4 = 1/10 Given that log10 2 = 0.3010 the value of log10 5 is ? 0.3241 0.6911 0.6990 0.7525 Correct Answer :0.6990 Explanation :log105 = log10(10/2) = log1010 - log102 = 1-0.3010 = 0.6990 The value of log 128 - log 8 / log 4 is ? A) 7 B) 5 C) 2 D) 1 Correct Answer :2 Explanation :log 128 - log 8 / log 4 => log (128/8) / log 4 => log 16 / log 4 => log 42 / log 4 => 2 log 4 / log 4 => 2 What is the solution of the equation xlog10(10/3) + log103= log10(2 + 3x ) + x ? A) 10 B) 3 C) 1 D) 0 Correct Answer :0 Explanation :xlog10(10/3) + log103= log10(2 + 3x ) + x log10(10/3)x + log103= log10(2 + 3x ) + log1010x [ because logaa =1, log am = m log a] log10(10/3)x * 3= log10(2 + 3x ) * 10x [ because logca + logcb = logcab ] (10/3)x * 3= (2 + 3x ) * 10x 3*10x/3x = (2 + 3x ) * 10x 3*10x = 3x * 10x *(2 + 3x ) 3 = 3x *(2 + 3x ) Let 3x = y Then 3 = y *(2 + y ) y2 + 2y - 3=0 ( y + 3)( y - 1) = 0 y = -3, 1 that is 3x = -3, 1 consider 3x = 1 [3x ≠ -3] 3x = 10 Hence x = 0