Simplifying and Solving Exponential Expressions: Tips and Tricks

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Discussion Overview

The discussion focuses on simplifying and solving exponential expressions, specifically addressing two problems presented by a participant. The scope includes mathematical reasoning and problem-solving techniques related to exponential forms.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Exploratory

Main Points Raised

  • One participant questions how to simplify the expression (3*square root of 2)^square root of 2 and expresses uncertainty about solving the equation 3^(power of 2*x)-1=3^(power of x) + 2.
  • Another participant suggests that the first expression cannot be simplified further and proposes defining y=3^x to recast the second equation for potential solving.
  • A different participant references a textbook (Glencoe Algebra 2) that indicates the first expression can be simplified but does not provide the method.
  • One participant proposes using a variable to represent the exponent in the first expression to make it clearer and suggests applying laws of exponents.
  • Another participant finds the resulting expression from their work to be complicated and likens it to a calculator exercise.
  • One participant shares their derived expression, (3^(1/2))*2^((2^(1/2))/2), and notes it appears neat on paper despite its complexity.
  • A later reply reminds participants that they can use LaTeX formatting in their posts for clearer mathematical representation.

Areas of Agreement / Disagreement

Participants express differing views on the simplification of the first expression, with some asserting it cannot be simplified further while others reference external sources suggesting otherwise. The second equation also remains unresolved, with various approaches proposed but no consensus on a solution.

Contextual Notes

There are limitations in the discussion regarding the clarity of the simplification process and the methods suggested, as well as the potential dependence on definitions from external sources. The mathematical steps involved in solving the second equation are not fully resolved.

amd123
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1. (3*square root of 2)^square root of 2 How do I simplify this and other exponential expressions?
2. 3^(power of 2*x)-1=3^(power of x) + 2 How do i solve this?

I don't know how to attempt it...Help please
 
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Regarding your first question: you can't, really. Subjectively, there's no "simpler" form than what you already have.

Regarding your second question: define y=3^x, and recast your equation in terms of y. Can you solve this?
 
according to glencoe algebra 2 number 1 can be simplified even more but they don't tell HOW?

no https://www.physicsforums.com/latex_images/16/1681321-1.png that's what its supposed to look like, i have to find x
 
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Try this: instead of 2^(1/2), use some variable, r, for the (1/2). Now you have
something like (3*2^r)^(2^r), convert this into ordinary algebraic notation so it is easier to understand; and then use your laws of exponents.
 
Actually what I obtain is not much clearer. Example seems like a calculator exercise.
 
Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.
Three to the square root of two power, multiplied by two to the [square root of two] over two power. It may read complicated, but it looks neat on my paper.
 
symbolipoint said:
Now, I find this:

(3^(1/2))*2^((2^(1/2))/2 )

It would look better if I had access to TEX right now.

You can always use latex in your posts by typing [tex]your latex code [ /tex]. (without the space in front of the /)[/tex]
 

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