if $\sqrt{2\sqrt{t-2}} = \sqrt[4]{7 - t}$ then find t.
We have, in exponential form :
2^(1/2) (t - 2)^(1/4) = (7 - t)^(1/4) take each side to the 4th power
2^2 ( t - 2) = 7- t
4 ( t - 2) = (7 - t)
4t - 8 = 7 - t rearrange as
5t = 15
t = 3
Start by squaring both sides.
2sqrt(t-2) = sqrt(7-t)
sqrt(4t-8) = sqrt(7-t)
4t - 8 = 7 - t
=^._.^=
