How can I determine if two log functions are equivalent?

In summary, to graph a logarithmic function, determine the base and plot points on a graph using the logarithm function. The domain is all positive real numbers and the range is all real numbers. To find the intercepts, set y or x equal to 0 and solve. A calculator can be used to graph a logarithmic function, but it is important to understand the steps by hand. The direction of the graph can be determined by the base and exponent of the logarithmic function.
  • #1
merikukri
9
0
Graph Y1 = log (X^26) & Y2 = 26 Log (X) Are they Equivalent ?

I drew the graph using X values ( -5, -4, -3, ... , 4, 5 )
and I got graphs, but don't know how to account for any differences in two functions..
Can anyone in here help
 
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  • #2
When working with logs, you should know that,

log(AB) = log(A) + log(B)

What does that tell you about,
log(AA) = ??

what about.
log(AAA) = ?

etc.
 
  • #3
Why not show us your table of values?
 

FAQ: How can I determine if two log functions are equivalent?

1. How do I graph a logarithmic function?

To graph a logarithmic function, first determine the base of the logarithm. Then, choose a few values for the input (x) and calculate the corresponding output (y) using the logarithm function. Plot these points on a graph and connect them with a smooth curve. Be sure to label the axes and indicate the scale of the graph.

2. What is the domain and range of a logarithmic function?

The domain of a logarithmic function is all positive real numbers, since the logarithm of a negative number is undefined. The range is all real numbers, since the output of a logarithm can be any real number depending on the input.

3. How do I find the x and y-intercepts of a logarithmic function graph?

The x-intercept of a logarithmic function graph is found by setting y equal to 0 and solving for x. The y-intercept is found by setting x equal to 0 and solving for y. Keep in mind that the x-intercept may not always be a real number, depending on the base and exponent of the logarithmic function.

4. Can I use a calculator to graph a logarithmic function?

Yes, most scientific and graphing calculators have a logarithm function button that allows you to quickly graph a logarithmic function. However, it is still important to understand the steps involved in graphing a logarithmic function by hand.

5. How can I tell if a logarithmic function is increasing or decreasing?

A logarithmic function with a base greater than 1 will be increasing, meaning the graph will move from left to right. A logarithmic function with a base between 0 and 1 will be decreasing, meaning the graph will move from right to left. You can also determine the direction of the graph by looking at the sign of the exponent in the function.

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