Question
Simplify exactly
log_2 1/16
log_2 1/16
Answers
Damon
base^log x = x
2^z = 1/16
where z is log_2 (1/16)
but we know that
2^0 = 1
2^-1 = 1/2
2^-2 = 1/4
2^-3 = 1/8
2^-4 = 1/16 ah ha
so 2^(-4) = 1/16
z = -4
and log_2 (1/16 ) = -4
check:
b^log_b(x) = x
2^-4 = 1/16 ???
1/2^4 = 1/16 sure enough
2^z = 1/16
where z is log_2 (1/16)
but we know that
2^0 = 1
2^-1 = 1/2
2^-2 = 1/4
2^-3 = 1/8
2^-4 = 1/16 ah ha
so 2^(-4) = 1/16
z = -4
and log_2 (1/16 ) = -4
check:
b^log_b(x) = x
2^-4 = 1/16 ???
1/2^4 = 1/16 sure enough