CBSE Class 9 Answered

If (2.5)^x = (0.025)^y = 10³

Find the value of 1/x – 1/y

Asked by haroonrashidgkp | 29 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 | 30 Jul, 2018, 09:39: AM

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