I need to graph the function,
y = log(root 3)2x
I did...now I need to graph the inverse. What is that?
Are these base 10 logs?
Do you mean
y = log (2x)^(1/3)
?
If so then it
is
y = (1/3) log (2x)
inverse
x = (1/3) log (2y)
3 x = log 2 y
10^(3x) = 2 y
y = (1/2)(1000)(10^x)
y = 500 (10^x)
I am sorry, base 3..
log base 3 of (2x)
y = log(3)2x means that
3^y = 2x, so
x = (1/2)*3^y is the inverse function
You could also write it in inverse function notation as
f^-1(x) = (1/2)*3^x
To graph the inverse of a function, you need to first find the inverse function, and then plot the points on the graph by swapping the x and y coordinates of the original function.
The given function is y = log₃(2x). To find its inverse, you need to interchange the x and y variables and solve for y.
Step 1: Swap x and y
x = log₃(2y)
Step 2: Solve for y
To isolate y, you need to get rid of the logarithm and solve the equation. Rewrite the equation in exponential form:
3^x = 2y
Multiply both sides by 1/2 to isolate y:
y = 3^(x/2)
Now you have the inverse function, y = 3^(x/2).
To graph the inverse function, plot points by choosing different x-values and calculating their corresponding y-values using the inverse function equation. Since the original function involves logarithms, there are some restrictions on the values you can choose for x.
For example, if you choose x = 0, the corresponding y-value will be y = 3^(0/2) = 3^0 = 1. So one point on the graph of the inverse function is (0, 1). Similarly, you can choose additional x-values and calculate the corresponding y-values to plot more points.
Once you have multiple points, connect them with a smooth curve to get the graph of the inverse function.