Tricky!

Algebra Level 3

$\large 2^x = 2^{46} - 2^{45} - 2^{44} - \ldots - 2^{-44} - 2^{-45} - 2^{-46}$

What is the value of $x$ that satisfy the equation above?

-46 -93 0 -92

2 solutions

Shaurya Chats
Jul 21, 2014

Simple... $2^{46} - 2^{45}$ is $2^{45}$ , $2^{45} - 2^{44}$ is $2^{44}$ , and so on.... you'll finally get $2^{-46}$ .

I did the same ;)

VAIBHAV borale - 6 years, 10 months ago

Can you explain more?

Akshat Sharda - 5 years, 10 months ago

I'm getting 1 at the end

Akshat Sharda - 5 years, 10 months ago

Harshvardhan Kalra
Jul 22, 2014

Multiply both sides by 2^46, then leaving 2^92 aside, form a G.P. series which reduces to 2^(x+46)=1, giving x=(-46).