Question

3(2^2x+3)-5(2^x+2)-156=0

Answer 1

Answer: $x=3.0206$

Step-by-step explanation:

Given

$3(2^{2x}+3)-5(2^x+2)-156=0$

Replace $2^x$ by $y$

We can write

$\Rightarrow 3(y^2+3)-5(y+2)-156=0\\\Rightarrow 3y^2+9-5y-10-156=0\\\Rightarrow 3y^2-5y-157=0\\\\\Rightarrow y=\dfrac{5\pm \sqrt{25-4(3)(-157)}}{2\times 3}\\\\\Rightarrow y=\dfrac{5+43.69}{6}\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206$