This question assumes you understand the definition and the laws of logarithms.
\na) To find the $x$-intercept, substitute $y=0$ into the equation: $0=\\log_{\\var{b}}(x)$ which is equivalent to $\\var{b}^0=x$, i.e. $x=1$. Therefore, the $x$-intercept is the point $(1,0)$.
\nb) Substitute $y=1$ into the equation: $1=\\log_{\\var{b}}(x)$ which is equivalent to $\\var{b}^1=x$, i.e. $x=\\var{b}$. Therefore, another easily found point is $(\\var{b},1)$.
\nc) Let's investigate what happens to the value of $y$ when the value of $x$ is increased by a factor of $\\var{b}$:
\n\\[\\log_{\\var{b}}(\\var{b}x)=\\log_{\\var{b}}(\\var{b})+\\log_{\\var{b}}(x)=1+\\log_{\\var{b}}(x)\\]
\nThis is the old $y$ value plus 1, so we can say that $y$ is increased by 1.
\nd) As $x$ gets larger and larger, $y$ gets larger and larger. Even though the rate of increase slows, $y$ continues to grow without bound.
\ne) An asymptote is a line or curve that approaches a given curve arbitrarily closely. For the curve $y=\\log_{\\var{b}}(x)$ the closer $x$ gets to zero (approaching from the right), the smaller $y$ gets (without bound). In other words, as $x$ approaches $0$ from the right, $y$ approaches negative infinity. This means that the asymptote for $y=\\log_{\\var{b}}(x)$ is the line $x=0$ (the $y$-axis).
\nf) Given all the information above, it should be clear that the graph should look like
\n{graph1(1)}
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The $x$-intercept of $y=\\log_{\\var{b}}(x)$ is the point $\\large($[[0]], [[1]]$\\large)$.
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\nThe logarithm you will be working with for this question is \\[y=\\log_{\\var{b}}(x).\\]
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