What is the domain and range of log3 (1-x)?
I will be happy to critique your thinking.
To assist you, consider
log (-4) log (0) log 25
Those are to the base 10, changing to another base just changes the numbers, not the function.
To find the domain and range of the function log3(1-x), let's first start by understanding what a logarithmic function represents.
The logarithmic function log(base a) of a number x is used to determine the exponent to which the base (a) must be raised to obtain the number x. In this case, the base is 3.
Before we analyze the domain and range, we need to consider the limitations of the logarithmic function. The argument (the number inside the parentheses) of a logarithmic function must be positive for the function to be defined. Otherwise, it will result in an error.
Now let's determine the domain, which represents all possible values for the input of the function. In our case, the argument of the logarithmic function is (1-x).
To avoid any errors, the argument must be greater than 0. Hence, we solve the inequality:
1 - x > 0
By isolating x, we find the range of valid values for (1-x):
x < 1
Therefore, the domain of the function log3(1-x) is all real numbers x such that x < 1.
Next, let's determine the range, which represents all possible values for the output of the function.
In logarithmic functions, the base determines the restriction on the range. Since the base is 3, any positive value can be obtained as the output.
Hence, the range of the function log3(1-x) is all real numbers greater than zero.
In summary:
- Domain: x < 1
- Range: All positive real numbers
Let me know if you need any further clarification or have other questions!