Calculate Directly

Question

Log (base 4) 2 + log (base 16) 2

Answer 1

since 16=4^2, log_4 = 2log_16
so, converting all to base 4 logs,

log4(2) + 1/2 log4(2)

Since 2 = √4, log4(2) = 1/2, and we have

1/2 + 1/2 (1/2) = 1/2 + 1/4 = 3/4

or, looking at it another way,
2 = √4, so log4(2) = 1/2
2 = ∜16, so log16(2) = 1/4

1/2 + 1/4 = 3/4