Hard Exponent problem from MGMAT

[tomintampa]

If 4^4x = 1600, what is the value of (4^x–1)^2?

Help, I'm confused. Thank you.

[JessT]

Is this a data sufficiency question?

[cubicle]

if the question is

4^4x = 1600

it can not be solved without using logarithm

i.e. 4^4x = 4^3 * 5^2

4xlog 4 = 3log4+2log5

if q is 4^4 *x = 1600
then 4^4 *x = 4^3 *5^2

or x = 6.25

what are the options ?

[bkparikh]

Are either of these correct? I had trouble deciphering the notation of the question.

4^(4x) = 1600
(4^(2x))^2 = 1600
4^(2x) = 40 - having taken the sqrt of each side

If 2nd part is [4^(x-1)]^2 then
= 4^(2x-2)
= 4^(2x) / 4^2
= 40/16

If 2nd part is (4^x - 1)^2 then
= 4^2x - 2*4^x + 1
= 40 - 2*sqrt(40) + 1
= 41 - 2*sqrt(40)

Remember that (a^m)^n = a^(mn)

[tomintampa]

this is correct:


If 2nd part is [4^(x-1)]^2 then
= 4^(2x-2)
= 4^(2x) / 4^2
= 40/16