Question

for which values of a the following equation has only one solution

Answer 1

\[\huge \log(x^2+2ax)-\log(8x-6a-3)=0\]

Answer 2

log(x^2+2ax)−log(8x−6a−3)=0
log((x^2+2ax)/(8x−6a−3)) = log 1
cancel out the log's
(x^2+2ax)/(8x−6a−3) = 1
cross product!
x^2+2ax = 8x−6a−3
x^2+2ax - 8x + 6a + 3 = 0
x^2 + (2a-8)x + 6a + 3 = 0
take the discriminant (D) = 0
(2a-8)^2 - 4(1)(6a+3) = 0
4a^2 - 56a + 52 = 0
a^2 - 14a + 13 = 0
solve for a then ...