Question

If 2.3 =(0.23). =1000! Find 1/x_1/y

Answer 1

2.3^x = 0.23^y = 1000 
x = log (base 2.3) of 1000 = log (1000) / log(2.3) 
y = log (base 0.23) of 1000 = log(1000) / log(0.23) 
 use base 10 for those logs, so we have: 
x = 3 / log(2.3) 
y = 3 / log(0.23) 
1/x = log(2.3) / 3 
1/y = log(0.23) / 3 
(1/x) - (1/y) = (log(2.3) - log(0.23)) / 3 
(1/x) - (1/y) = (log(2.3/0.23)) / 3 
(1/x) - (1/y) = (log(10)) / 3 
(1/x) - (1/y) = 1/3