Some logarithmic identities to remember:
[tex]nlog_ab = log_ab^{n}[/tex]
[tex]log_ab - log_ac = log_a(\frac{b}{c})[/tex]
If we rewrite the equality, we get:
[tex]log_3y = \frac{1}{3}log_364 - log_316[/tex]
[tex]log_3y = log_{3}64^{\frac{1}{3}} - log_{3}16[/tex]
[tex]log_3y = log_34 - log{3}16[/tex]
Using the second identity, we produce:
[tex]log_{3}y = log_{3}(\frac{4}{16}[/tex]
We can say that:
[tex]y = \frac{4}{16} = \frac{1}{4}[/tex], since we are comparing the two statements.
