Question

Solve : x ( $3^x$ - 1) ($4^x$ - 16 ) ( x- 5) < 0

• A. x ( - , 2) (5 , )
• B. x ( 2 ,5)
• C. x (2 , 5)
• D. x ( - , -3) ( 5 , )

Answer 1

The correct option is B

x ( 2 ,5)

Let given expression be E = x ( $3^x$ - 1)( $4^x$ -16 )(x - 5)

$3^x$ - 1 = 0 $\Rightarrow$ x = 0

$4^x$ - 16 = 0 $\Rightarrow$ x = 2

Now , mark x = 0 , 2, 5 on real number line. Sign of E starts with postive sign from right hand side.Also at x = 0 , two factors , namely x & $3^x$- 1 are zero.

Hence, sign of E does not change while crossing x = 0

Sign scheme of E is hown below.

From above figure, we have E < O for x $ϵ$ (2 ,5)