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Question

Let the domains of x of the given equation loga(2x+3x)0 for (i) a>1 be [n,pk)(pk,) (ii) 0<a<1 be [,m). Find m+n+p+k

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Solution

loga(2x+3x)0x32

Since, a>1

2x+3x1

2x+3x

x+30

x[3,32)(32,]

Also,

For 0<a<1 then

0<2x+3x<1

2x+3<x

x+3<0

x(,3]

Given, m=3,n=3,p=3,k=2

m+n+p+k=3+3+3+2=11

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