(2.3)^x=(0.23)^y=1000, find the value of 1/x-1/y?
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2.3^x = 0.23^y = 1000
Apply logarithms:
x Log 2.3 = y Log 0.23 = Log 1000
x Log 2.3 = y (Log 2.3/10 ) = 3
x Log 2.3 = y (Log 2.3 - Log 10) = 3
1/x = (Log 2.3)/3
1/y = (Log 2.3 -1)/3 = (Log 2.3)/3 - 1/3
1/y = 1/x - 1/3
1/x - 1/y = 1/3
Apply logarithms:
x Log 2.3 = y Log 0.23 = Log 1000
x Log 2.3 = y (Log 2.3/10 ) = 3
x Log 2.3 = y (Log 2.3 - Log 10) = 3
1/x = (Log 2.3)/3
1/y = (Log 2.3 -1)/3 = (Log 2.3)/3 - 1/3
1/y = 1/x - 1/3
1/x - 1/y = 1/3
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