(2.3)^x=(0.23)^y=1000 then what is the value of (1/x) - (1/y)?
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(2.3)^x=1000
(23/10)^x = 10³
23/10 = (10)^3/x----(1)
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(0.23)^y =10³
23/100 = (10)^3/y ---(2)
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(1) / (2)
(23/10) / (23/100) = (10)^3/x /(10)^3/y
⇒10^1 = (10) ^3/x - 3/y
1= 3/x-3/y
1=3(1/x-1/y)
1/3 = 1/x- 1/y
∴
1/x-1/y = 1/3
(23/10)^x = 10³
23/10 = (10)^3/x----(1)
===================
(0.23)^y =10³
23/100 = (10)^3/y ---(2)
=====================
(1) / (2)
(23/10) / (23/100) = (10)^3/x /(10)^3/y
⇒10^1 = (10) ^3/x - 3/y
1= 3/x-3/y
1=3(1/x-1/y)
1/3 = 1/x- 1/y
∴
1/x-1/y = 1/3
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