I need some help with logarithmic functions?

Question

f(x) = 3 log (3-x)

I have to first rearrange it properly and then graph it. I have no idea how to do this and have been trying for hours. any help would be appreciated.

Answer 1

I'm going to assume you're dealing log base 10, because (1) the calculator's log button is base 10, and (2) log base e has its own name, ln (natural log).

f(x) = 3 log (3 - x)

Do you know how to make graphs symmetric across the line
y = x? Those are the properties of inverses. This is one way to graph this.

First, find the inverse. Make f(x) = y.

y = 3 log(3 - x).

Swap the x and y terms.

x = 3 log(3 - y)

Solve for y in terms of x.

(x/3) = log(3 - y)
10^(x/3) = 3 - y
y = -(10)^(x/3) + 3

All you have to do is graph that exponential function, make a dashed line of y = x, and create a new graph symmetric across the y = x line to the graph you just made.

Answer 2

I don't know exactly what you need to arrange. You just substitute values of x in, evaluate 3-x, take the log of that and triple it. That's the "y" on the graph. Beware though that there are no such things as logs of 0 or negative numbers, so your domain for x ends at <3.

Answer 3

Get your graphing calculator.

Remember that the log of a negative number or zero is undefined,

so graph only with x < 3

Answer 4

to help yourself with graphing first graph logx. if you do not know how to do that look at simple graph in book. Then graph log(-x). IHere inverse graph by y axis. Then graph log(-x +3), here you just move all points by 3 units to the left. And finally graph 3log(3-x). Here you stretch graph vertically by 3.

Answer 5

f(x) = 3log(3 - x)

this can be written as

f(x) = log((3 - x)^3)

for a graph, go to http://www.calculator.com/calcs/GCalc.html

and you can type it in as log((3 - x)^3), assuming you don't have a base to worry about.