Explain how you could graph each function by applying transformations.(a) y = log(x -2) + 7 (b) y = -3logx (c) y = log(-3x)-5

(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