find the value of N if log32 N= -3/5
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Answer:
log
3
2,log
3
(2
x
−5),log
3
(2
x
−
2
7
) are in arithmetic progression.
⇒log
3
2+log
3
(2
x
−
2
7
)=2×log
3
(2
x
−5)
⇒log
3
(2×(2
x
−
2
7
))=log
3
(2
x
−5)
2
⇒2
x+1
−7=(2
x
−5)
2
i.e. 2
x+1
−7=2
2x
−5×2
x+1
+25
i.e. 2
2x
−6×2
x+1
+32=0
i.e. 2
2x
−12×2
x
+32=0
i.e. (2
x
−4)×(2
x
−8)=0
i.e. 2
x
=4,8orx=2,3
However, when x is 2,2
x
−5 becomes −1 which is not allowed inside logarithm.
Hence x=3.
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