1. if P(t)=3e^2t, for what value does P(t)= 2P(2)

Question

2. Find all x for which the square root of log (x)= log square root of x

thanks!!

Answer 1

1. If P(t) =3P(2)
then 3e^(2t) = 2(3e^(4t)
e^(2t) = 2 (e^2t)^2
let e^2t = y
y = 2y^2
2y^2 - y = 0
y(2y -1) = 0
y = 0 or y = 1/2

e^2t = 0 ---> no solution
or
e^2t = 1/2
ln (e^2t) = ln (1/2) = ln1 - ln2 = -ln2
2t = -ln2
t = (-1/2)ln 2

2. √(log(x)) = log (√x) = log x^(1/2) = (1/2) logx
let logx = y
√ y = (1/2)y
y = (1/4)y^2
4y = y^2
y^2 - 4y = 0
y (y - 4) = 0
y = 0 or y = 4

logx = 0 or logx = 4
x = 10^0 = 1 OR x = 10^4 = 10000

Answer 2

My error for #1, see "bobpursley's" answer
http://www.jiskha.com/display.cgi?id=1355365995