Question

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

Answer 1

Answer:
`x=3.0206`

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=(5\pm √(25-4(3)(-157)))/(2* 3)\\\\\Rightarrow y=(5+43.69)/(6)\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206`