Question

How do you do this problem?

Answer 1

Some logarithmic identities to remember:

`nlog_ab = log_ab^(n)`

`log_ab - log_ac = log_a((b)/(c))`

If we rewrite the equality, we get:

`log_3y = (1)/(3)log_364 - log_316`

`log_3y = log_(3)64^{(1)/(3)} - log_(3)16`

`log_3y = log_34 - log{3}16`

Using the second identity, we produce:

`log_(3)y = log_(3)((4)/(16)`

We can say that:

`y = (4)/(16) = (1)/(4)`, since we are comparing the two statements.