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The value of log_{2}3 x log_{ 3}2 x log_{3}4 x log_{4}3 is ? 
1 1 Explanation : log_{a}x = log_{b }x/log_{b }a=log x/log a Thus, log_{2}3 x log_{ 3}2 x log_{3}4 x log_{4}3 
The value of log 9/8  log 27/32 + log3/4 is ? 
0 0 Explanation : log_{a}(xy) = log_{a} x + log_{a} y Thus, log 9/8  log 27/32 + log3/4 => log [(9/8) /(27/32)] + log3/4 
The equation log_{a}x + log_{a} (1+x)=0 can be written as ? 
x^{2} + x  1 = 0 x^{2} + x  1 = 0 Explanation : log_{a}(xy) = log_{a} x + log_{a} y So, log_{a}x + log_{a}(1+x) = 0 
if log 3 = 0.477 and (1000)^{x} = 3, then x equals to ? 
0.159 0.159 Explanation : log_{a}(x^{p})=p(log_{a}x) (1000)^{x} = 3 

Find the value of log_{9} 81  log_{4} 32 ? 
1 / 2  1 / 2 Explanation : log_{a}x = log_{b }x/log_{b }a=log x/log a. log_{9} 81  log_{4} 32 
log_{1/3} 81 is equal to ? 
 27  4 Explanation : log_{x} x=1 y=x^{x }is equivalent to, log_{x}y = log_{x}x ⇒ log_{x}y =x Let, log_{1/3}81 = x 
The value of log_{10} 0.000001 is ? 
6  6 Explanation : log_{10} 10^{6} = 6 

The value of log_{6} log_{5} 15625 is ? 
1 1 Explanation : log_{6} log_{5}15625 = log_{6} log_{5}(5)^{6} 
If log_{10000}x = 1/4, then x is ? 
1 / 100 1 / 10 Explanation : log_{10}^{4}x = 1/4 
Given that log_{10} 2 = 0.3010 the value of log_{10} 5 is ? 
0.3241 0.6990 Explanation : log_{10}5 = log_{10}(10/2) 
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 
What is the solution of the equation xlog_{10}(10/3) + log_{10}3= log_{10}(2 + 3^{x} ) + x ? 
A) 10 B) 3 C) 1 D) 0 Correct Answer : 0 Explanation : xlog_{10}(10/3) + log_{10}3= log_{10}(2 + 3^{x} ) + x consider 3^{x} = 1 [3^{x} ≠ 3] 