Question

Solve: ( $5^x$ - 1)( $2^x$ - 8) < 0

• A. x ( - , 0) ∪ (3, )
• B. x ( 2 ,5)
• C. x ( 0 ,3)
• D. x ( - , 2) (5 , )

Answer 1

The correct option is C

x ( 0 ,3)

Let given expression be E = ($5^x$ - 1)( $2^x$ - 8)

$5^x-1=0\Rightarrow$ x = 0

$2^x-8=0\Rightarrow$ x = 3

Now, mark x = 0, 3, on real number line. Sign of E starts with postive sign from right hand side.

Also at x = 0, two factors, namely x & $5^x$ - 1 are zero.

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

Sign scheme of E is shown below

From above figure, we have E < 0 for x $ϵ$ (0 ,3)