IPMAT Rohtak 2019 (QA) - If 2, (2x - 1), (2x + 3) are in A.P, then x is equal to ____ | PYQs + Solutions

IPMAT Rohtak 2019

Algebra

Progression & Series

Easy

If $\log 2, \log (2x - 1), \log (2x + 3)$ are in A.P, then $x$ is equal to ____

\frac{5}{2}

\log_2 5

\log_3 2

Correct Option: 1

When

a,b,c

are in A.P,

2b=a+c

Hence,

2[log(2x-1)]=log(2)+log(2x+3)

We know that

n.log(y)=log(y)^n

and

log(a)+log(b)=log(ab)

So,

log(2x-1)^2=log(4x+6)

So,

(2x-1)^2=4x+6

4x^2+1-4x=4x+6

\newline

4x^2-8x-5=0

\newline

4x^2-10x+2x-5=0

\newline

2x(2x-5)+1(2x-5)=0

\newline

(2x+1)(2x-5)=0

x=-\frac{1}{2}

\frac{5}{2}

But log values are always positive, hence

x=\frac{5}{2}