Question #db4ff

1 Answer
Feb 4, 2018

#k = -1/40000#

Explanation:

If we let #u = 10^x#, then #u^2 = 10^(2x) = 100^x #

The equation becomes:

#u^2= (10)^-2u+k#

Writing the quadratic in standard form:

#u^2-1/100u-k = 0#

For there to be one and only one solution the discriminant must be 0:

#b^2-4(a)(c) = (-1/100)^2 -4(1)(-k) = 0#

#4k = -1/10000#

#k = -1/40000#