No idea - solve log_a(x) defined only for 0<a<1 and a>1

In summary, the conversation discusses solving the expression log_a(x) for a range of values between 0 and 1 and values greater than 1. The responder is confused about the question as loga(x) is an expression and cannot be solved. The original poster clarifies that the question is likely about solving an equation or inequality involving this expression.
  • #1
Luxm
3
0
No idea -- solve log_a(x) defined only for 0<a<1 and a>1

Homework Statement


Describe how to solve log_a(x) defined only for 0<a<1 and a>1
 
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  • #2
Solve log_a(x) for what? Your question doesn't make sense to me.
 
  • #3
It is basically a discussion question where I have to describe how to solve log_a x defined only for 0 < a < 1 and a > 1
 
  • #4
Luxm said:

Homework Statement


Describe how to solve log_a(x) defined only for 0<a<1 and a>1

Your question makes no sense. loga(x) is an expression. You can solve an equation or an inequality, but you can't solve an expression.
 
  • #5
Here is a snip of it, but yes I'll go back and ask him about the problem.
 

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1. What does the notation log_a(x) mean?

The notation log_a(x) represents the logarithm base a of x. This means that a is raised to a certain power in order to get x.

2. Why is log_a(x) only defined for 01?

This is because the logarithm function is only defined for positive numbers, and when a<0, the result would be a complex number. Additionally, when a=0 or a=1, the logarithm function would be undefined.

3. How do you solve a logarithm with a base between 0 and 1?

To solve a logarithm with a base between 0 and 1, you can use the change of base formula: log_a(x) = log_b(x) / log_b(a), where b is a base greater than 1. This allows you to rewrite the logarithm in terms of a base that is easier to work with.

4. Can you give an example of solving a logarithm with a base between 0 and 1?

For example, to solve log_(1/2)(8), we can rewrite it as log_2(8)/log_2(1/2). Since log_2(1/2) is equal to -1, we can simplify the expression to -log_2(8), which is equal to -3.

5. Why is it important to restrict the base of a logarithm to be between 0 and 1?

Restricting the base to be between 0 and 1 helps to ensure that the logarithm function remains well-behaved and avoids any complex or undefined outputs. It also allows for easier manipulation and calculation of logarithms using the change of base formula.

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