What is x?

[youenr]

2^x-2^x-2=3(2^13)

solution is 15 but I can't find it!

[ind_sam]

2^x - 2^x-2 = 3(2^13)
=> 2^(x-2+2) - 2^x-2 = 3(2^13) (x can be written as x-2+2)
=> (2^x-2).(2^2) - 2^x-2 = 3(2^13)
=> 2^x-2(2^2-1) = 3(2^13)
=> 2^x-2(3) = 3(2^13) => x - 2 = 13 => x = 15

Hope it helps :)

[youenr]

thanks for your reply.
Unfortunately I am still confuse :)
how x can be written as x-2+2?
I started with 2^x-2 which for me equal 2x/4, but I am stuck after!
thanks

[jnelson0612]

thanks for your reply.
Unfortunately I am still confuse :)
how x can be written as x-2+2?
I started with 2^x-2 which for me equal 2x/4, but I am stuck after!
thanks

Okay, let's try to write this out so it is less confusing:
2^x - 2^(x-2)=3(2^13)

So on the left we have two values, 2^x and 2^(x-2). We want to subtract the second from the first. Whenever we want to add or subtract values with the same bases, express both of them in terms of the SMALLER one. Thus:
2^x = 2^2 * 2^(x-2), which is 4 * 2^(x-2)
AND
2^(x-2) = 1 * 2^(x-2)

So really, it's [4 * 2^(x-2)] - [1 * 2^(x-2)]= 3 * 2^(x-2)

Thus, 3 * 2^(x-2) = 3 * 2^13.
So x-2=13, or x=15.

Hope this helps!

[youenr]

Thanks, got it!

[jnelson0612]

Great, thanks!