AAAGH i dont understand ANY of these questions , please someone help, its desperate, thankssssss tonnes

in these questions i will type logs as log[2]16

= log to the base 2 of 16.

**3) ** Given that p= log[q]16

express in terms of p:

a) log[q]2

b) log[q](8q)

**4)**

a) Given that log[3] x = 2, determine the value of x

b) Calculate the value of y for which 2log[3]y - log[3](y+4) = 2

c) Calculate the values of z for which log[3]z = 4log[z]3

**6)**

Solve, giving your answers as exact fractions, the simultaneous equations:

8^y = 4 ^2x+3

log[2]y = log[2]x + 4

**7)**

Find the values of x for which log[3]x - 2log[x]3 = 1

**8)**

Solve the equation

log[3](2-3x) = log[9](6x^2 - 19x +2)

**9)**

If xy=64 and log[x]y + log[y]x = 5/2, find x and y.

**12)**

a) Given that 3 + 2log[2]x = log[2]y, show that y = 8x^2

b) Hence, or otherwise, find the roots alpha and beta, where alpha < beta, of the equation 3 + 2log[2]x = log[2](14x - 3)

c) Show that log[2]alpha = -2

d) Calculate log[2]beta, giving your answer to 3 s.f.