assuming T=t
reemmber
alogb=log(b^a)
and loga-logb=log(a/b)
and [tex]a^{log_a(b)}=b[/tex]
[tex]2log_b(t)-log_b(2)=log_b(2t+6)[/tex]
[tex]log_b(t^2)-log_b(2)=log_b(2t+6)[/tex]
[tex]log_b( \frac{t^2}{2})=log_b(2t+6) [/tex]
raise both sides to the b power
[tex] \frac{t^2}{2} =2t+6[/tex]
times 2 both sides
t²=4t+12
t²-4t-12=0
(t-6)(t+2)=0
t=-2 or 6
