Logarithms

1.If logx (0.1) = -1/3, then the value of x is: 
a) 10 
b) 100 
c) 1000 
d) 1/1000  

2.If ax = by, then:
a) log(a/b) = x/y 
b) log(a) / log(b) = x/y 
c) log(a) / log(b) = y/x 
d) None of these 
  
3.If log8 x + log8 (1/6) = 1/3 then the value of x is: 
a) 12 
b) 16 
c) 18 
d) 24   

4.If log x + log y = log (x + y), then: 
a) x = y 
b) xy=1 
c) y = (x-1)/x 
d) y = x/(x-1)   

5.If log10 7 = a, then log10(1/70) is equal to: 
a) -(1 + a) 
b) (1 + a)-1 
c) a/10 
d) 1/10a  

6.If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is: 
a) a2+b2 = 7ab 
b) a2-b2 = 7ab 
c) (a+b)2 = 2 
d) (a+b)/3 = (1/2)(a+b)  

7.If log x = log 3 + 2 log 2- (3/4) log 16. The value of x is: 
a) 1/2 
b) 1 
c) 3/2 
d) 2  
e) None of these   

8.If log x =(1/2) log y = (1/5) log z, the value of x4y3z-2 is: 
a) 0 
b) 1 
c) 2 
d) 3 
e) None of these   

9.If log10000 x = -1/4, then x is given by: 
a) 1/100 
b) 1/10    
c) 1/20 
d) none of these   

10.The value of 3-1/2 log3(9) is: 
a) 3 
b) 1/3-
c) 2/3 
d) none of these  

11.loge xy - loge |x| equals to: 
a) loge x 
b) loge |x| 
c) - loge x 
d) none of these   

12.The value of (loga n) / (logab n) is given by: 
a) 1 + loga b 
b) 1 + logb a 
c) loga b 
d) logb a   

13.If (a^4 - 2a^2b^2 + b^4)x-1 = (a-b)^2x (a+b)-2, then x equals to: 
a) (a - b) / (a + b) 
b) log (a2 - b2) 
c) log (a + b) / log (a - b) 
d) log (a - b) / log (a + b)