Answers

2015-07-01T19:10:38+05:30
(2.3) ^{x} =(0.23) ^{y} =1000 =  10^{3}  \\ (2.3)^{x} = 10^{3}
Now consider the log in both side of the equation,
log(2.3) ^{x} = log(10) ^{3}  \\ x.log(2.3)= 3.log10 \\ xlog(2.3)=3 \\ x= \frac{3}{log(2.3)}
And 1/x = log(2.3)/3
Now,
    (0.23)^{y} =10^{3}
now we find y according to above process
y = 3/log(0.23)
A/Q,
              \frac{1}{x} - \frac{1}{y} = \frac{log( 2.3) }{3} - \frac{log(0.23)}{3}  \\  \frac{log(2.3)-log(0.23)}{3} = \frac{Log \frac{2.3}{0.23} }{3}  = \frac{log 10}{3}= \frac{1}{3}
5 4 5