Solve 4 ^ x - 2^(2(x-1)) 8^((2/3)*(x-1))>52

Evaluate

4^{x} - 2^{2 (x - 1)} \times 8^{\frac{2}{3} (x - 1)} > 52

Simplify

More Steps

4^{x} - 2^{4 x - 4} > 52

Move the expression to the left side

4^{x} - 2^{4 x - 4} - 52 > 0

Rewrite the expression

4^{x} - \frac{1}{16} \times 2^{4 x} - 52 > 0

Rewrite the expression

2^{2 x} - \frac{1}{16} \times 2^{4 x} - 52 > 0

Solve the equation using substitution t = 2^{2 x}

t - \frac{1}{16} t^{2} - 52 > 0

Move the constant to the right side

t - \frac{1}{16} t^{2} > 0 - (- 52)

Add the terms

t - \frac{1}{16} t^{2} > 52

Evaluate

t^{2} - 16 t < - 832

Add the same value to both sides

t^{2} - 16 t + 64 < - 832 + 64

Evaluate

t^{2} - 16 t + 64 < - 768

Evaluate

(t - 8)^{2} < - 768

Calculate

t \in / R

Solution

x \in / R

Alternative Form

No real solution

Solve the inequality