Solving Limit Involving Logarithms

Thread starter Revelation
Start date Oct 23, 2008
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Limit Logarithms

In summary, a limit involving logarithms is finding the value a function approaches as its input approaches a specific value, with the function containing a logarithm expression. To solve such limits, you can use algebraic manipulation, properties of logarithms, or L'Hopital's rule. The change of base formula can also be used to simplify the limit. Special cases to consider include logarithms with a base of 1 or a negative argument, which may require different methods to solve. To check your solution, you can plug in the limit value and compare it to the calculated limit, or use a graphing calculator to visually verify your solution.

Oct 23, 2008

Revelation

Hi! I'm having trouble solving this limit:

lim x->infinite ln(1+2^x)ln(1+3/x)

Revelation

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Oct 23, 2008

Dick

Science Advisor

Homework Helper

The limit has the form infinity*0. That would suggest l'Hopital's rule, wouldn't it? Change the form to 0/0 or infinity/infinity.

1. What is a limit involving logarithms?

A limit involving logarithms is a mathematical concept that involves finding the value that a function approaches as its input approaches a specific value. In this case, the function contains a logarithm expression.

2. How do I solve a limit involving logarithms?

To solve a limit involving logarithms, you can use algebraic manipulation, the properties of logarithms, or L'Hopital's rule. It is important to carefully analyze the function and determine which method would be most appropriate.

3. Can I use the change of base formula when solving limits involving logarithms?

Yes, the change of base formula can be used to simplify a limit involving logarithms. This formula states that log_b(x) = log_a(x) / log_a(b), where a and b are any positive bases.

4. Are there any special cases to consider when solving limits involving logarithms?

Yes, there are a few special cases to consider. One is when the limit involves a logarithm with a base of 1, which is undefined. Another is when the limit involves a logarithm with a negative argument, which is undefined for real numbers. In these cases, you may need to use other methods to solve the limit.

5. How can I check if my solution to a limit involving logarithms is correct?

You can check your solution by plugging in the limit value into the original function and comparing it to your calculated limit. If they are equal, then your solution is likely correct. You can also use a graphing calculator to visualize the function and see if your solution aligns with the graph.