(a)

Consider the given function

\(y=\log(x−2)+7\)

To find the transformation of the graph of the given function

First, draw the graph of the following function

\(y=\log(x)\)

Now, take horizontal shift right 2 units of the above

So,

\(y=\log(x−2)\)

Again, take vertical shift up by 7 units of the above

So,

\(y=\log(x−2)+7\)

Hence, above are the required transformations.

(b)

Consider the given function

\(y=−3 \log x\)

To find the transformation of the graph of the given function

\(yyy=== \log x −\log x\) (Reflection about the x−axis) \(−3 \log x\) (Dilation with scale factor 3 −stretched vertical)

Hence, the required transformations for the graph of the given function are reflection and dilation.

(c)

Consider the given function

\(y= \log (−3x)−5\)

To find the transformation of the graph of the given function

\(y= \log (x)y= \log (3x)\) (Dilation by scaling factor 3−stretched horizontal)\(y= \log (−3x)\) ( Reflection about the y−axis )\(y= \log (−3x) −5\) (Vertical shift down 5 units )

Hence, the required transformations for the graph of the given function are dilation by scaling factor 3 units, reflection about the y-axis, and vertical shift down 5 units