Posted by **Rebekah** on Wednesday, December 12, 2012 at 8:04pm.

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

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

thanks!!

- logarithms -
**Reiny**, Thursday, December 13, 2012 at 12:39am
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

- logarithms -
**Reiny**, Thursday, December 13, 2012 at 12:48am
My error for #1, see "bobpursley's" answer

http://www.jiskha.com/display.cgi?id=1355365995

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