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

  • Thread starter brenfox
  • Start date
In summary, to solve the equation (3.4)^(2x+3) = 8.5, one can take the logarithm of both sides and solve for x, which gives a solution of x = -0.626.
  • #1

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)

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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  • #2
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"?
  • #3
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!
  • #4
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).
  • #5
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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