so:

(1)=> lnx - (ln3.5 +ln2) -1/2^x = -log(10^1/128)

however:

ln3.5 +ln2 = ln(3.5*2) = ln7

and:

log(10^1/128) = 1/128 = (128 = 2^7) = 1/2^7

so:

lnx -1/2^x = ln7 -1/2^7 (3)

I now define a function f(x) = lnx -1/2^x

I will skip the proof, but just take it that f(x) is

strictly increasing(that means that for every x,y that belong to (0, +infinity), with x < y , f(x) < f(y). This also means that: x = y <=> f(x) = f(y) )

(3) => f(x) = f(7) => x = 7

that means y = 7*1000 => y = 7000

EDIT:

http://prnt.sc/f7xz7teh, that's pretty much accurate

Edited 5/15/2017 06:47:31