Solve $4^{- x + 0.5} - {7.2}^{- x} < 4$

Open in App

Solution

$4^{- x + 0.5} - {7.2}^{- x} < 4$
$2^{- 2 + 1} - {7.2}^{- x} < 4$
$2^{- x} = t, t ϵ (0, \infty)$
$\Rightarrow 2. t^{2} - 7 t - 4 < 0$
$\Rightarrow 2 t^{2} - 8 t + t - 4 < 0$
$\Rightarrow (2 t + 1) (t - 4) < 0$
$t ϵ (- \frac{1}{2}, 4)$
$\Rightarrow 2^{- x} ϵ (0, 4)$
$\Rightarrow {log}_{2} 2^{- x} ϵ ({log}_{2} (0), {log}_{2} 4)$
$\Rightarrow - x ϵ (- \infty, 2)$
$\Rightarrow x ϵ (- 2, \infty)$

Suggest Corrections

Similar questions

x ϵ R

4^{- x + 0.5} - {7.2}^{- x} - 4 < 0

4^{- x + 0.5} - 7 \cdot 2^{- x} - 4 < 0

8^{l o g_{2} (x - 4 y)} = 1, 4^{x - 2 y} - {7.2}^{x - 2 y} = 8

s i n^{4} x + c o s^{4} x = s i n 2 x - 0.5.

{log}_{0.5} (4 - x) ⩾ {log}_{0.5} 2 - {log}_{0.5} (x - 1)

Join BYJU'S Learning Program