skynugurq7

2022-07-03

Answer exactly: $4\cdot {1.1}^{x}=8.5$
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:
$x=\frac{\mathrm{log}\frac{8.5}{4}}{\mathrm{log}1.1}$
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?

Miles Mueller

Expert

$\begin{array}{rl}4×{1.1}^{x}& =8.5\\ {1.1}^{x}& =\frac{8.5}{4}\\ x\mathrm{log}1.1& =\mathrm{log}\left(\frac{8.5}{4}\right)\\ x& =\frac{\mathrm{log}\left(\frac{8.5}{4}\right)}{\mathrm{log}1.1}\\ x& ={\mathrm{log}}_{1.1}\left(\frac{8.5}{4}\right)\end{array}$
What you have done seems to be correct. The last step isn't necessary.

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