How much more exponentially is 680^4 vs 340^4. My calculator says 10.XXXXX does this mean that 640^4 is only 10 times more than 340^4?

680⁴   =   (2 * 340)⁴

 

680⁴   =   2⁴ * 340⁴

 

680⁴   =   16 * 340⁴

 

In other words,  680⁴  is  16  times  340⁴

If you want to know how much you'd have to add to  340⁴  to get  680⁴, we can solve this equation for  x:

 

x + 340⁴  =  680⁴

 

x  =  680⁴ - 340⁴

 

x  =  200450400000

 

So

 

200450400000 + 340⁴  =  680⁴

 

In other words,  680⁴  is  200450400000  more than  340⁴

 

If you want to know what power must  340⁴  be raised to to equal  680⁴,  we can solve this equation for  x:

 

(340⁴)^x   =   680⁴

 

340^x  =  680

 

x  ≈  1.1189

 

So

 

(340⁴)^1.1189  ≈  680⁴