Simplify the Expression: (log₄5 + log₄2)/(3log₄2)

The sum property $\log_4 5 + \log_4 2 = \log_4(5 \times 2) = \log_4 10$ combines the numerator into a single logarithm, making the fraction easier to work with.

The power rule converts $3\log_4 2$ into $\log_4 2^3 = \log_4 8$. This is crucial because it allows us to use the change of base formula!

This uses the change of base property: $\frac{\log_a x}{\log_a y} = \log_y x$. So $\frac{\log_4 10}{\log_4 8} = \log_8 10$.

You could use decimal approximations, but that's much harder and less exact. The algebraic approach using logarithm properties gives you the exact answer!

Remember the pattern: $\frac{\log_a x}{\log_a y} = \log_y x$. The denominator's argument (y) becomes the new base!