Solving x in 3.4^2x + 3 = 8.5: (-0.626)

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Homework Help Overview

The problem involves solving the equation (3.4)^(2x+3) = 8.5 for the variable x, with participants discussing the correct interpretation of the equation and the steps involved in the solution process.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the correct formatting of the equation, with some questioning whether the original poster accurately represented the equation. There are discussions about the use of logarithms and the steps taken to isolate x.

Discussion Status

There is an ongoing clarification regarding the equation's format, with some participants suggesting that the original expression may have been miswritten. Guidance has been offered on how to approach the problem using logarithmic properties, although no consensus on the correct interpretation has been reached.

Contextual Notes

Participants are addressing potential misunderstandings related to the notation used in the equation, specifically the placement of parentheses and the representation of exponents. There is also mention of formatting preferences for presenting equations in the forum.

brenfox
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Homework Statement


(3.4)^2x+3 = 8.5. Solve for x

Homework Equations

The Attempt at a Solution


3.4^2x = 8.5/3.4^3 ( divide the equation by 3.4^3. This bit i am not sure about)

2xlog3.4 = log (8.5/3.4^3

x = log (8.5)- 3log(3.4) / 2 log (3.4)

=0.929-1.594/1.063
x = -0.626

This seems to work out when i plug it into the original equation.
Is there an insert equation icon on the template. Can`t find it!
 
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I think you meant to say:

(3.4)^(2x+3) = 8.5. Solve for x.

Right? If not you need to edit your post to fix it.

What do you mean by "an insert equation icon"?
 
Looked at the question again and I have wrote it correctly. 3.4 is in parentheses. Not sure why this is so.

An equation icon makes my equations look neater if you know what I mean!
 
brenfox said:
Looked at the question again and I have wrote it correctly.
Are you saying that the original looks exactly like that, using the caret symbol instead of a superscript? Seems unlikely, so what you have posted is probably a rendition. But what you posted is equivalent to 3.42x+3. If you meant 3.42x+3 then you can write it as 3.4^(2x+3). And I feel it is a little simpler to take logs first then solve 2x+3 = log(8.5)/log(3.4).
 
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Apologies jedishrfu, I have wrote it down wrong. Thanks haruspex, I should have used parentheses after the caret symbol. You live and learn!
 

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