The justification of the third step in her proof of the property of logarithms is; [tex]log_{b} (b^{xy})[/tex]; Power rule of exponents
From the full question, the second step stopped at;
[tex]log_{b} (b^{x} . b^{y} )[/tex]
Now, according to Power Rule for Exponents we know that (a^m)ⁿ = a^(m*n). That means that to raise a number with an exponent to a power, we will multiply the exponent times the power.
Thus, [tex]log_{b} (b^{x} . b^{y} )[/tex] will give us [tex]log_{b} (b^{xy})[/tex] using power rule of exponents
Read more about Properties of Logarithms at; https://brainly.com/question/14765705
