Graphing Logarithmic Functions

Need homework help? Connect with our top Graphing Logarithmic Functions Experts!

To create a logarithmic function, you need to devise a set of points and then pull a smooth curve through those points.

To graph, a logarithmic function, follow the step-by-step guide here:

  1. Write the function in logarithmic form. A logarithmic function has the form y = log_a(x), where a is the logarithm base. For instance, the function y = log_2(x) is a logarithmic function with base 2.
  2. Pick a series of values for x and calculate the corresponding values of y. Logarithmic functions are specified only for positive values of x, so you should select a series of x-values that are all positive. For example, you might choose x = 1, x = 2, x = 4, and so on. For each value of x, compute the corresponding value of y using the formula y = log_a(x).
  3. Plan the points on the graph. On the x-axis, plan the values of x that you chose in step 2. On the y-axis, plan the corresponding values of y.
  4. Draw a smooth curve through the points. Logarithmic functions contain a "staircase" shape, with each step depicting the power of the base. To draw the curve, join the points with a smooth curve that follows the general shape of the function.

It is important to remember that the graph of a logarithmic function is always a curve, not a straight line. The curve gets closer and closer to the x-axis as the x gets larger, but it will never touch the x-axis. This is because the values of y in a logarithmic function always approach 0 as x gets larger, but they never really reach 0.

Browse More Topics

Volume of a Cylinder Surface Area of a Cylinder How to Convert Ounces to Gallons Volume of a Cone Area of the Triangle Domain and Range Volume of a Sphere Interval Notation Lines, Line Segment and Rays Axis of Symmetry of a Parabola Volume of a Pyramid Surface Area of Pyramid Geometric Series 30-60-90 Triangles Distance Formula Sum and Difference of a Cube Degree to Radian Measure Coplanar Graphic Square Root Functions 45-45-90 Triangle Graphing Cosine Function Surface Area of a Prism Radian to Degree Mean, Median, and Mode Powers of 10 Rounding Decimals Converse Inverse and Contrapositive Surface area of a cone Vertex of a Parabola Surface area of a sphere Decimals Reflections Fractions to Percent One-to-One Function Quadrilaterals Absolute Value Function Law of Sines Weight Mass Law of Cosines Tangent Function Prime and Composite Number Linear Pair Complementary Angles Supplementary Angles Reflective, Symmetric, and Transitive Properties Rate of Change Volume of a Prism Completing The Square End behavior of Function Vertical Angles

30 minutes Live Session FREE!