Question 1110101
what you will find is:


log2(x-4) is the same as log2(x), but shifted to the right 4 units on a graph.


an example will show you what i mean.


when x = 6, the value of y = log2(x) is 2.585


when x = 10, the value of y = log2(x-4) is 5.585.


the value of y = log2(x-4) when x = 10 is the same value of y = log2(x) when x = 6, except that the value is 3 units higher.


how is this so?


well, when x = 6, y = log2(x) becomes log2(6) and, when x = 10, y = log2(x-4) becomes y = log2(10 - 6) which becomes log2(6).


the difference is the + 3 added to y = log2(x-4).


it raises the value of y + 3 units to make it y = 5.585, rather than y = 2.585.


here's what the graph of this example looks like.


<img src = "http://theo.x10hosting.com/2018/022103.jpg" alt="$$$" >


this relationship happens with all equations, not just log equations.


here's a reference on transformation of algebraic equations.


those rules apply to log functions as well.


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