Given that logbase2 a+logbase2 b=3 , calculate all the possible integer values of a if b is

Question

also an integer value. Explain your reasoning.

Answer 1

log₂ a + log₂ b = 3
log₂ (ab) = 3
ab = 2^3 = 8

using positive integer values, all possibilties for
(a,b) are
(1,8)
(2,4)
(4,2) and
(8,1)

testing one of them: a=4, b=2

LS = log₂4 +log₂ 2
= 2 + 1
= 3
= RS

Answer 2

1=24
yes