Logarithms and Exponentials Help Please Asap! ! !
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.
