solution set for the inequality log10²x-3(log10x)(log10(x-2))+2log10²(x-2)<0 is
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MATHS
The complete solution set of the inequality log
3
(x+2)(x+4)+log
1/3
(x+2)<
2
1
log
3
7 is equal to
December 30, 2019avatar
Kanishka Ranjan
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ANSWER
log
3
(x+2)(x+4)+log
1/3
(x+2)<(1/2)log
3
7
Clearly, this is defined for x>−2⇒(i)
⇒
log3
log(x+2)
+
log3
log(x+4)
+
log(
3
1
)
log(x+2)
<
2
1
2
1
log3
log7
,[∵log(ab)=loga+logb&log
a
b=
log
b
a
1
]
⇒
log3
log(x+2)
+
log3
log(x+4)
−
log3
log(x+2)
<
log3
log7
⇒
log3
log(x+4)
<
log3
log7
⇒log
(x+4)<log
(7),∵log3>0
⇒x+4<7
⇒x<3⇒(ii)
Thus from (i) and (ii)
The solution set is (−2,3)
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