Question 283758
As a base 5 logarithm, the only values for y you will be able to find will those for x's that are known powers of 5. 1 is a power of 5. It is {{{5^0}}}. For x's greater than 1 use 5, 25 and 125 (which are powers of 5 should know (or be able to figure out). For x's between 0 and 1 use 1/5, 1/25 and 1/125. But these values will not make the graph easy. It will be hard to graph x values of 25 and 125 on the same graph as x values of 1/25 and 1/125 unless you have an immense piece of graph paper.<br>
A more practical approach would be to use the base conversion formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to rewrite the base 5 logarithm as an equivalent expression of base 10 logarithms:
{{{y = log((x))/log((5))}}}
Now we can pick any (positive) numbers we want for x and use our calculator to find the value for y. I'll leave that up to you to do.<br>
For the asymptote, logarithmic functions have a vertical asymptote for the value of x that makes the argument 0. It works like this because arguments of logarithms cannot be zero or negative. So zero represents the highest invalid argument. X must have values that result in arguments greater than zero.<br>
Your argument is simply x so x=0 (i.e. the y-axis) is a vertical asymptote for the graph of your function.