Question

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

Answer 1

Take log =>

log(2.3)^x = log (0.23)^y = log t = log1000
x*log2.3 = y*log 0.23 = log t = 3

x = logt/log2.3 --> 1/x = log2.3/logt = log2.3 / 3

1/x - 1/y = 1/3*( log2.3 - log 0.23)
1/x - 1/y = 1/3*(log (2.3/0.23))
1/x - 1/y = 1/3* log 10

1/x - 1/y = 1/3