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{{ printedBook.courseTrack.name }} {{ printedBook.name }} When equations are solved graphically, the variable terms are isolated on one side of the equation, with the constant term on the other. In the given equation, this is already the case. Therefore, we do not need to rearrange the equation before constructing the function rule. $f(x)=g_{2}(5x) $ To draw the graph of a logarithmic function, we can follow a three-step process.

- Identify the base.
- Determine points on the graph.
- Plot the points and sketch the graph.

Let's do it! Looking at the given function, we can see that the base is $b=2.$ $f(x)=g_{2}(5x) $ Using the base, we will construct a table of values.

$x$ | $g_{2}(5x)$ | $f(x)=g_{2}(5x)$ |
---|---|---|

$0.1$ | $g_{2}(5(0.1))$ | $-1$ |

$0.2$ | $g_{2}(5(0.2))$ | $0$ |

$0.4$ | $g_{2}(5(0.4))$ | $1$ |

$0.8$ | $g_{2}(5(0.8))$ | $2$ |

Let's plot the points $(0.1,-1),$ $(0.2,0),$ $(0.4,1),$ and $(0.8,2),$ and connect them with a smooth curve.

The solution to the equation is the $x-$value of the point whose $y-$coordinate is $2.$ We'll mark this point on the graph.

From the diagram, we see that the graphs intersect at $x≈0.8.$ We can verify this solution by substituting it into the original equation.$g_{2}(5x)=2$

Substitute$x=0.8$

$g_{2}(5(0.8))=2$

MultiplyMultiply

$g_{2}(4)=2$

WritePowWrite as a power

$g_{2}(2_{2})=2$

$g_{2}(2_{m})=m$

$2=2$