Question

What is the logarithmic function of the graph? show work

Answer 1

If the function of the logarithmic graph is written as

$y=\log _ax^b$

Since the graph has been shifted to the right from the origin by 5 units

Then

$y=b\log _a(x-5)$

a is base, b is coefficient, y and x are coordinates on the line

Taking a point on the line, say (21, 2)

x= 21 and y = 2

$\begin{gathered} y=\text{ }\log _a(x-5)^b \\ 2\text{ = }\log _a(21-5)^b \\ a^2=(16)^b \\ (a^2)^1=(4^2)^b \\ \text{Equating the base and the power} \\ a\text{ = 4 and b= 1} \end{gathered}$

If the base is 4 and the coefficient is 1

The logarithmic function of the graph is

$y=\text{ }\log _4(x-5)$