7. If (2.3)X = (0.23)) = 1000 then find
the value of ---
1
1
ху
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Answer:
Given that,
2.3^x=0.23^y=1000
Now,
2.3^x=1000 and 0.23^y=1000
Applying log on both sides we get,
log2.3^x=log1000
xlog2.3=log10^3
xlog(23/10)=3
log(23/10)=3/x.....................................1
and,
log0.23^y=log1000
ylog(23/100)=log10^3
ylog(23/100)=3
log(23/100)=3/y..................................2
By eq1-eq2 we get,
log(23/10)-log(23/100)=3/x-3/y
log{(23/10)/(23/100}=3(1/x-1/y)
log10=3(1/x-1/y)
1=3(1/x-1/y)
1/3=1/x-1/y.
Hence value of 1/x-1/y=1/3.
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