# How do you graph g(x) = 1/4log_2 (x - 4) - 3?

Feb 11, 2017

See graph and explanation.

#### Explanation:

To make g real, $x > 4$.

x-intercept ( y = 0 ) :4100, from, ${\log}_{2} \left(x - 4\right) = 12$, giving x=4+2^12

Converting to ln,

g=1/4(ln(x-4)/ln 2)-3 and the Socratic graph is created.

Ax $x \to \infty , g \to \infty$.

Also, as $x \to 4 , y \to - \infty$, revealing the asymptote x = 4..

x-intercept ( y = 8 ) :4100, from, ${\log}_{2} \left(x - 4\right) = 12$, giving x=4+2^12

graph{(1/4ln(x-4)/ln2-3-y)=0 [0, 10000, -5, 5]}

The graph is no to uniform scale in both directions. Yet, it reveals features