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I'm having a little trouble formatting the title, but I think it's understandable. It's my first question here, and I'll do what I can to use the MathJaX notation correctly. Also, English is not my primary language, but I'll do my best to get myself understood.

I have the following equation: $$4 \cdot 1.1^x = 8.5$$ They want the answer to be exact. Unfortunately I haven't been able to get further than this: $$x = \frac{\log \frac{8.5}4}{\log 1.1}$$ I'm not even sure this is correct, but I think so. Anyone have a good idea how to get further? Maybe I need to start all over?

Alex Wertheim
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Anders
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    This is sufficient. You could evaluate numerically to get an approximate solution but it's not necessary. – Cameron Williams Aug 14 '13 at 18:17
  • Welcome to MSE! Your use of MathJax looks good - I've made a few small edits to your post to make it just a bit more readable, and to make your notation consistent. As far as your problem goes, I'm not sure how much more you can simplify that. That looks to me as exact as you can get! You could simplify $\log(8.5/4) = \log(8.5) - \log(4)$, but I don't think that adds anything meaningful – Alex Wertheim Aug 14 '13 at 18:17
  • Thank you both for your help. @AWertheim I checked your edit so from now on I should be able to provide better titles :) – Anders Aug 14 '13 at 18:35

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\begin{align} 4\times 1.1^x&=8.5\\ 1.1^x&=\frac{8.5}{4}\\ x\log 1.1&=\log \left(\frac{8.5}{4}\right)\\ x&=\dfrac{\log \left(\frac{8.5}{4}\right)}{\log 1.1}\\ x&=\log_{1.1} {\left(\frac{8.5}{4}\right)}\\ \end{align} What you have done seems to be correct. The last step isn't necessary.

Inquest
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  • Actually, steps (3) and (4) aren't necessary. You could get (5) from (2) immediately by the definition of log function. – Kaster Aug 14 '13 at 18:29
  • @Kaster, I know. I was just trying to be a bit more methodical. – Inquest Aug 14 '13 at 18:31
  • Thank you Inquest. I'll stick to the solution you've provided then, skipping the last step. I thought that I somehow could get rid of the log statements and end up with a regular fraction somehow. – Anders Aug 14 '13 at 18:33