Question

2logbT - logb 2 = logb(2t + 6)

Answer 1

assuming T=t

reemmber
alogb=log(b^a)
and loga-logb=log(a/b)
and
`a^(log_a(b))=b`



`2log_b(t)-log_b(2)=log_b(2t+6)`

`log_b(t^2)-log_b(2)=log_b(2t+6)`

`log_b( (t^2)/(2))=log_b(2t+6)`
raise both sides to the b power

`(t^2)/(2) =2t+6`
times 2 both sides
t²=4t+12
t²-4t-12=0
(t-6)(t+2)=0
t=-2 or 6