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

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The equation 3.4^(2x+3) = 8.5 is solved by first isolating the exponential term and then applying logarithms. The solution process involves dividing both sides by 3.4^3 and using logarithmic properties to simplify the equation. The final result for x is calculated as -0.626, which checks out when substituted back into the original equation. There was some confusion regarding the notation used in the equation, with discussions about the correct formatting of exponents. Overall, the key takeaway is the importance of proper notation and the logarithmic approach to solving exponential equations.
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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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Likes jedishrfu
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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