![]() In your case, b was equal to 2 and x was equal to (x + 3). It's based on the basic definition of logs that states that: The exponential form is equivalent to the log form. They both result in the same identical curved line on the graph. The log form of the equation and the exponential form of the equation are both shown. To plot the points manually, you use the exponential form of the equation and select values for y and then solve for corresponding values of x. The second is scaled soyou can see the point (29,5). The first is scaled so you can see the vertical asymptote and the points of (-1,1) and (5,3). I also put a dashed line where the vertical asymptote is. I plotted the essential points so you can visually see what i calculated above. Superimposed on that is the graph of the exponential equation. The grpah of the log equation is shown below: The value of x will never get less than -3, so you have a vertical asymptote at x = -3. If you look at the equation of x = 2^y - 3, you will see that as y becomes a very large negative number, the value of 2^y gets very close to 0 and so the value of x gets very close to -3. Space them out so you get a good idea of the overall shape of the graph. If you need more points, you sould just plot more points. To manually graph this equation without resorting logs using your calculator, you would pick 3 random values for y and then solve for x. ![]() ![]() It explains when logarithmic graphs with base 2 are preferred to logarithmic graphs with base 10. Solve this equation for x and you get x = 2^y - 3. This post offers reasons for using logarithmic scales, also called log scales, on charts and graphs. Let y = f(x) and the equation becomes y = log(2,x+3). You can put this solution on YOUR website! ![]()
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