How do logarithms and exponential functions relate?

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In summary, Wayne and Gareth are looking for help in understanding and explaining log laws to their daughter who is struggling with solving equations involving logs in AS maths. They also shared a relatable story about their own struggles with math. Two laws that were not covered in the suggested link were mentioned and another helpful link was provided.
  • #1
acceler8
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hi, out daughter doing AS maths is unsure of exponentail functions and how they relate to natural logs. she finds it really hard to solve equations involving logs.

can you help explain the log laws to me so we understand and explain them to her. we hate the embarassed feeling of not knowing what to say.


xxxxx Wayne and Gareth
 
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  • #3
(Unrelated response) Don't feel too embarassed, there is always a worse case than your own right? My dad couldn't help me with math past algebra I despite having a statistics major :) (thank goodness he is working in a field that doesn't require it or someone would be screwed)

Maybe a more specific question would help, but two laws I didn't see covered in the above link (hyperphysics is a great website by the way) were the summation laws: ln(a) + ln(b) = ln(a*b) or ln(a) + ln([tex]b^{-1}[/tex]) = ln(a/b)
 
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  • #4
Here's another link that explains logarithms and the logarithmic rules.

http://oakroadsystems.com/math/loglaws.htm
 
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1. What are exponentials and logarithms?

Exponentials and logarithms are mathematical operations that are used to represent and manipulate numbers that are very large or very small. Exponentials involve raising a base number to a certain power, while logarithms involve finding the power to which a base number must be raised to result in a given number.

2. How are exponentials and logarithms related?

Exponentials and logarithms are inverse operations of each other. This means that they "undo" each other, and can be used to solve equations involving exponential or logarithmic functions.

3. What are some real-world applications of exponentials and logarithms?

Exponentials and logarithms are used in a variety of fields, including finance, biology, and physics. They can be used to model population growth, radioactive decay, and compound interest, among other things.

4. How do I solve equations involving exponentials and logarithms?

When solving equations involving exponentials and logarithms, the key is to use the properties of these operations to "move" the variables to one side of the equation. This usually involves taking logarithms of both sides of the equation, or using the power rule to simplify an exponential expression.

5. Are there any tips for working with exponentials and logarithms?

One helpful tip is to remember the basic properties of exponentials and logarithms, such as the power rule and the product/quotient rules. Also, it can be useful to convert logarithmic expressions into exponential form and vice versa, as this can make them easier to work with.

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