If 625^(-x) +5^(-2x) + 5^(-4x) = 15, what is the value of x? Select the correct option:
A) -4 B) -1/4 C) 0 D) 1/4 E) 4
We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.   Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....   With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.   With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.   With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.   With Answer C, anything to the '0 power' is 1, so we'd have   1+1+1= 
<gadget id="calculator">  1+1+1</gadget>
<output>3</output>
3. This is not 15. Eliminate C.   -4
<result>A</result>
If 625^(-x) +5^(-2x) + 5^(-4x) = 15, what is the value of x?