Evaluate the following given log4 u 12 and log4 v 2 log2 u

Evaluate the following given log_4 (u) = 1/2 and log_4 (v) = 2. log_2 (u^3 v) log_16 (u/v^2)

Solution

log₄u=1/2

log₂u/log₂4 = log₂u/2=1/2

log₂u=1

log₄v=2

log₂v/log₂4 = log₂v/2

log₂v=4

a. log₂u³v   =   3 log₂u   +   log₂v    =     3+4=7

b.log₁₆(u/v²)

log₁₆u=log₄u/log₄16   = log₄u/2   1/4

log₁₆v= log₄v/log₄16 = log₄v/2 =1

log₁₆(u/v²) = log₁₆u - log₁₆v²   =    1/4   - 2 = -7/2