If (2.5)x = (0.025)y = 103

Find the value of 1/x – 1/y

Asked by haroonrashidgkp | 29th Jul, 2018, 07:26: PM

Expert Answer:

(2.5)x = (0.025)y = 103 
begin mathsize 16px style log space 2.5 to the power of straight x space equals space log space 0.025 to the power of straight y space equals space log space 10 cubed
xlog space 25 over 10 space equals space straight y cross times log space 25 over 1000 space equals space 3 log space 10
xlog space 25 over 10 equals 3 log space 10
rightwards double arrow straight x open parentheses log space 25 space minus space log space 10 close parentheses equals 3 log space 10
rightwards double arrow straight x equals fraction numerator 3 log space 10 over denominator log space 25 space minus space log space 10 end fraction
rightwards double arrow 1 over straight x equals fraction numerator log space 25 space minus space log space 10 over denominator 3 log space 10 end fraction........ left parenthesis straight i right parenthesis
space straight y cross times log space 25 over 1000 space equals space 3 log space 10
rightwards double arrow straight y open parentheses log space 25 space minus space log space 1000 close parentheses equals 3 log space 10
rightwards double arrow straight y equals fraction numerator 3 log space 10 over denominator log space 25 space minus space log space 1000 end fraction
rightwards double arrow 1 over straight y equals fraction numerator log space 25 space minus space log space 1000 over denominator 3 log space 10 end fraction....... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
1 over straight x minus 1 over straight y equals fraction numerator log space 25 space minus space log space 10 over denominator 3 log space 10 end fraction minus fraction numerator log space 25 space minus space log space 1000 over denominator 3 log space 10 end fraction
rightwards double arrow 1 over straight x minus 1 over straight y equals fraction numerator up diagonal strike log space 25 end strike space minus space 1 minus up diagonal strike log space 25 end strike minus 3 over denominator 3 log space 10 end fraction
rightwards double arrow 1 over straight x minus 1 over straight y equals fraction numerator negative 4 over denominator 3 end fraction end style

Answered by Sneha shidid | 30th Jul, 2018, 09:39: AM