$\frac{lo{g}_2^8+lo{g}_2^{16}-4lo{g}_2^2}{lo{g}_4^{16}}$
= $\frac{3lo{g}_2^2+4lo{g}_2^2-4lo{g}_{2}2}{2lo{g}_4^4}$
= $\frac{3+4-4}{2}$
= $\frac{3}{2}$

(b)

AP	GP
T${}_1$T${}_3$T${}_7$	T${}_1$T${}_2$T${}_3$

T${}_1$ + T${}_2$ = 6
a + a + d = 6
2a + d = 6.....(i)
a = a
a + 2d = ar, a + 6d = ar${}^2$
$\frac{a+2d}{a}=\frac{a+6d}{a+2d}$
(a + 2d)${}^2$ = $\frac{a+6d}{a+2d}$
(a + 2d)${}^2$ = a(a + 6d)
a${}^2$ + 4d${}^2$ + 4ad = a${}^2$ + 6ad
4d${}^2$ = 6ad - 4ad
4d${}^2$ = 2ad
$\frac{4d}{2}=\frac{2a}{2}$
a = 2d ......(ii)
from;
2a + d = 6
2(2d) + d = 6
4d + d = 6
5d = 6
d = $\frac{6}{5}$
= 1$\frac{1}{5}$
from; a = 2d
a = $\frac{2\times 6}{5}$
= $\frac{12}{5}$
= 2$\frac{2}{5}$
First term = 2$\frac{2}{5}$
Common difference = 1$\frac{4}{5}$