Finding unknown indices

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In summary, the conversation discusses the process for finding unknown indices, specifically in the equation 3^x=9. It mentions using the fact that 9=3^2 and taking the log base 3 of both sides to solve for x, which is equal to 2. It also notes that logarithms can be used for more complex equations, but for simpler ones, the relationship between the numbers can be used to solve without logarithms. However, if the answer is not an integer, logarithms are necessary.
  • #1
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I would be grateful if someone could tell me how to find unknown indices.

e.g 3^x=9

(i know it is 2 but i would like to know the process for use with larger numbers).

Thankyou in advance
 
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  • #2
3^x=9
therefore
9=3^2
get the log base 3 of both sides
x=2
 
  • #3
No, you used the fact x=2.

9 = 3^x

log 9 = log (3^x)

log 9 = x log 3

x = log9/log3 = 2

log can be to any base as long as they are the same. you will usually find base 10, or base e on your calculator. log base e is usually ln.
 
  • #4
No, you used the fact x=2.

1) 3x=9
As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam.

here are more examples (solve for x)
2) 5x = 625
3) 4*5x = 100
4) 2x = 8

If you use Logarithm, in the step log9/log3, you need to know the fact that 9 = 3^2 too, unless you use a caculator.
 
  • #5
1) 3x=9
As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam.

That's true as long as the "opposite" problem, finding the power, can be done easily- as long as the answer is an integer as in all of your examples.

To solve, for example 3x= 7, you will need to use logarithms.
 

1. What is the purpose of finding unknown indices?

Finding unknown indices is used to determine the values of variables in mathematical equations or to identify the elements in a data set. It allows us to solve problems and make predictions based on the information we have.

2. How do you find unknown indices in a mathematical equation?

To find unknown indices in a mathematical equation, you can use algebraic techniques such as isolating the variable on one side of the equation, using the distributive property, or combining like terms. You can also use substitution by plugging in known values for the variables to solve for the unknown one.

3. What strategies can be used to find unknown indices in a data set?

Some strategies for finding unknown indices in a data set include visualizing the data with graphs or charts, using statistical methods such as regression analysis, or using data mining techniques to identify patterns and relationships in the data.

4. How can finding unknown indices be applied in scientific research?

Finding unknown indices is crucial in scientific research as it allows scientists to analyze and interpret data, make predictions, and test hypotheses. It is used in various fields such as physics, chemistry, biology, and economics to understand complex systems and make informed decisions.

5. What are the potential challenges of finding unknown indices?

One of the main challenges of finding unknown indices is the possibility of making errors, especially when dealing with large and complex equations or datasets. Another challenge is that some problems may have multiple solutions, making it difficult to determine the correct one. Additionally, finding unknown indices may require a lot of time and resources, depending on the complexity of the problem.

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