How is the graph y = log(2x) + 3 related to the graph of y = log(x)?
It is stretched horizontally by a factor of 2 and translated up 3.
It is compressed horizontally by a factor of 2 and translated up 3.
It is stretched vertically by a factor of 2 and translated up 3.
It is compressed vertically by a factor of 2 and translated up 3.

Solution:

The function log(x) when transformed to log(2x), the transformation looks like this:

When three is added to log(2x) the transformation that takes place is shown below:

From the above graph we can conclude that by transforming log x into log(2x) the graph gets stretched vertically by a factor of 2, while adding 3 shifts the graph vertically upwards as apparent from the above diagram.

How is the graph y = log(2x) + 3 related to the graph of y = log(x)?

Summary:

The graph y = log(2x) + 3 related to the graph of y = log(x) in the following manner: It is compressed vertically by a factor of 2 and translated up 3.