log(base 2)16=8 true or false?

Write each of the problems into exponential notation and check ...

Rule:     log_bN = x    in exponential notation is     b^x = N

log₂16 = 8  in exponential notation is  2⁸ = 16     Is this true?

log₄2 = 1/2  in exponential notation is  4^1/2 = 2     Is this true?

2log₂47 = 47  can be written as  log₂47² = 47  in exponential notation is  2⁴⁷ = 47²     Is this true?

log₃9 + log₃(1/27)  =  1/2  can be written as  log₃(9·1/27)  =  1/2  which is  log₃(1/3) = 1/2

                                       in exponential notation is  3^1/2 = 1/3     Is this true?

$\log_216\\ = \log_22^4\\ = 4\\ \neq 8\\ \therefore\text{False.}$

$\log_42\\=\log_44^{1/2}\\=\frac{1}{2}\\ \therefore \text{True.}$

$2\log_2 47 \\ = \log_2 47^2\\ \neq 47\\ \therefore \text{False.}$

$\log_39 + \log_3\frac{1}{27}\\ =\log_33^2+\log_33^{-3}\\ = 2 + (-3)\\ = -1\\\neq 1/2\\ \therefore \text{False.}$