#4. Express the logarithm in terms of log2M and log2N:

Question

log2 1/MN

#5. Simplify:
log4 3 - log4 48

#6. Solve the equation:
loga x = 3/2loga 9 + loga 2

#7. Solve the equation:
logb (x2 + 7) = 2/3logb 64

#8. Solve the equation:
loga (3x + 5) - loga (x - 5) = loga 8

Answer 1

log2(1/MN) = -log2(MN) = -(log2M + log2N)

log4(3)-log4(48) = log4(3/48) = log4(1/16) = log4(4^-2) = -2

loga(x) = 3/2 loga(9) + loga(2)
loga(x) = loga(27*2)
x = 54

logb(x^2+7) = logb(16)
x^2+7 = 16
x^2 = 9
x = ±3

loga(3x+5)-loga(x-5) = loga(8)
loga((3x+5)/(x-5)) = loga(8)
(3x+5)/(x-5) = 8
x = 9