Graphing Logarithmic Functions

The graph of $y=\log (x)$ shows the value of the common logarithm for different $x$-values. To find the value of $\log (1),$ you read the $y$-value where $x$-value is equal to $1$, from the graph.

Since the point is placed on the $x$-axis, the $y$-value is $0.$

When we solve the equation $\log (x)=1,$ we know the value of the common logarithm, and instead find the $x$-value which gives the $y$-value equal to $1$. We start at the $y$-value of $1,$ go out to the graph and down to the $x$-axis, where we read the $x$-value $10$ from the axis.

Here we will rewrite the equation according to the common logarithm's definition, $b=\log (a)\iff a=10^b.$ $$10^y=5.5\iff y=\log (5.5)$$ As in the first part, find the value of $\log (5.5)$ by reading what $y$-value is when the $x$-value is equal to $5.5.$

We see that $y$ is approximately equal to $0.75.$