In my foundations of computing class, we were given a logarithm question which i don't quite understand. This is the question.
Given the logarithmic table values of the numbers x and y are ax and ay respectively, and that antilog(ax) = x and antilog(ay) = y then what does x * y equal in terms of ax and ay?
I'm just not quite sure what it's asking and would appreciate some guidance.
I'm not sure how to format it properly
You are given that $$ \operatorname{antilog} a_x = x \\ \operatorname{antilog} a_y = y $$ and are asked to express $x \times y$ in terms of $a_x$ and $a_y$. What you need to know is that $$ \operatorname{antilog} a = b^{a} $$ where $b$ is the base of the logarithm. Now, $$ x \times y = \operatorname{antilog} a_x \times \operatorname{antilog} a_y = b^{a_x} \times b^{a_y} $$ and I'll let you do the rest, using the basic properties of exponentials and the definition of $\operatorname{antilog}$.
