Question

(2.3)^x=(0.23)^y=1000, find the value of 1/x-1/y?

Answer 1

$(2.3) ^{x} =(0.23) ^{y} =1000 = 10^{3} \\ (2.3)^{x} = 10^{3}$
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,
             $\frac{1}{x} - \frac{1}{y} = \frac{log( 2.3) }{3} - \frac{log(0.23)}{3} \\ \frac{log(2.3)-log(0.23)}{3} = \frac{Log \frac{2.3}{0.23} }{3} = \frac{log 10}{3}= \frac{1}{3}$

Answer 2

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