Posted by Jonathan Burros on October 16, 2002 at 14:44:13:
In Reply to: problem posted by Joan on October 12, 2002 at 02:05:10:
: 7^(x-1)=(sqrt7)^(-2x^2)
: 7^(x-1)=7^[(1+(1/2))(-2x^2)]
: 7^(x-1)=7^[(3)x^2]
: (x-1)=[(3)x^2]
: I am not even close to the answer, now I am lost :(
7^(x-1)=(sqrt7)^(-2x^2)
The right side can be written
(7^(1/2))^(-2x^2)
= 7^(-x^2)
The origonal equation becomes
7^(x-1)= 7^(-x^2)
Equate the exponents on both sides
x-1 = -x^2
x^2 + x - 1 = 0
Solve this by the quadratic formula
x = [-1 +-sqrt[1^2 - 4(1)(-1)]]/[2(1)]
= (-1 +- sqrt 5)/2