Question 723447: How to graph f(x)= 1/2 log (base x) + 5
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How to graph f(x)= 1/2 log (base x) + 5
since the base is not known, use the base 10 curve normally on calculators as a reference.
Graph the basic log curve with y-axis as an asymptote and (1,0) as the x-intercept.
Logarithms with bases other than 10, still have the y-axis as an asymptote and also have the same x-intercept at (1,0). The difference with logs of different bases is that the lower the base the steeper the curve. You can visualize a family of log curves all having the y-axis as an asymptote and all going thru the x-axis at x=1, with the lower base logs below the higher base logs at x<1 and the other way around at x>1. To see this, get a graphing calculator and punch in logx and lnx which has a lower base.
..
For your log equation, the 1/2 coefficient multiplier compresses the curve slightly and the +5 raises the basic curve up 5 units, but does not change the position of the asymptote.
|
|
|
