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### Section 6.2 : Logarithm Functions

23. Sketch the graph of $$g\left( x \right) = \ln \left( x \right) - 4$$ .

Show Solution

For this problem all we need to do is recall the Transformations section from a couple of chapters ago. Using the “base” function of $$f\left( x \right) = \ln \left( x \right)$$ the function for this part can be written as,

$g\left( x \right) = \ln \left( x \right) - 4 = f\left( x \right) - 4$

Therefore, the graph for this part is just the graph of $$f\left( x \right)$$ shifted down by 4.

The graph of this function is shown below. The blue dashed line is the “base” function, $$f\left( x \right)$$, and the red solid line is the graph for this part, $$g\left( x \right)$$. 