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

[brenfox]

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!

 

[jedishrfu]

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"?

 

[brenfox]

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!

 

[haruspex]

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 3.4^2x+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).

 

[brenfox]

Apologies jedishrfu, I have wrote it down wrong. Thanks haruspex, I should have used parentheses after the caret symbol. You live and learn!