{{ item.displayTitle }}

No history yet!

Student

Teacher

{{ item.displayTitle }}

{{ item.subject.displayTitle }}

{{ searchError }}

{{ courseTrack.displayTitle }} {{ statistics.percent }}% Sign in to view progress

{{ printedBook.courseTrack.name }} {{ printedBook.name }} a

The graph of $y=g(x)$ shows the value of the common logarithm for different $x$-values. To find the value of $g(1),$ 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 $0.$

b

When we solve the equation $g(x)=1,$ 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.

c

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

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