how would i graph log3x the 3 is subscripted?
I remember that I had to make an X and Y chart and list the Domain and Range
Logarithms are the inverse of exponents. The base here is three and whatever to the right of the equals sign is the raised up exponent. You have the power to find coordinate point values by merely switching the input and output columns of this T-chart that you are mentioning. Come up with enough to plot a graph for the exponents and then just do a switcheroo (first (x,y) then (y,x)) in order to find what the logarithm graph would look like.
Can you show me how its done? I'm not very good at reading math directions and then figuring them out.
Can you work it out for me please?
by the definition of logs
if y = log 3x
then 3^y = x
so in making a table of values, pick any value of y and calculate x
make sure you enter those values under the correct columns for x and y
Keep you y values relatively small, since 3^y gets large in a hurry for positive y's
I suggest using y = 0, ±1,±2
if you have a calculator handy, you can of course use decimals for y as well
eg. y = .25
then 3^.25 = 1.316 = x
so (1.316,.25) would be a point.
Estimate its position on the graph.
To graph the function log₃x, follow these steps:
1. Determine the domain: Since log₃x is only defined for positive values of x (because the base 3 logarithm does not exist for negative or zero values), the domain of the function is x > 0.
2. Determine the range: The range of log₃x is all real numbers, so there is no restriction on the values of y.
3. Create an x-y chart:
- Choose a range of positive values for x. For instance, you can select x = 1, 3, 9, 27, 81, etc. Since log₃x is the inverse of 3ˣ, it is helpful to choose powers of 3 for x.
- Calculate the corresponding y-values using the given values of x by evaluating log₃x. For example, if x = 1, then y = log₃(1) = 0. If x = 3, then y = log₃(3) ≈ 0.631, and so on.
- Keep filling in the x-y chart until you have enough points to get a sense of the shape of the graph.
4. Plot the points on a graph. Place the values of x on the x-axis and the corresponding values of y on the y-axis.
5. Connect the plotted points to create the graph of log₃x. Since the base 3 logarithm function has a smooth curve, you can draw a smooth curve passing through the plotted points.
Remember, the base 3 logarithm function approaches negative infinity as x approaches 0 from the positive side and approaches positive infinity as x approaches infinity.