Solve the following equation: $$\frac{8^x + 27^x}{12^x + 18^x} = \frac{7}{6}$$  All I managed to do is rewrite the given equation in a simpler form: $$\frac{4^x}{6^x + 9^x} + \frac{9^x}{6^x + 4^x} = \frac{7}{6}$$  I don't know what should be done next.  Thank you in advance!
Find all real numbers $x$ for which $$\frac{8^x+27^x}{12^x+18^x}=\frac76$$  I have tried to fiddle with it as follows:   $$2^{3x} \cdot 6 +3^{3x} \cdot 6=12^x \cdot 7+18^x \cdot 7$$ $$ 3 \cdot 2^{3x+1}+ 2 \cdot 3^{3x+1}=7 \cdot 6^x(2^x+3^x)$$ Dividing both sides by $6$ gives us $$2^{3x}+3^{3x}=7 \cdot 6^{x-1}(2^x+3^x)$$  Is this helpful? If so, how should I proceed form here? If not any hints would be greatly appreciated.
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I have tried this command:  ogr2ogr -overwrite -f "ESRI Shapefile" -where OGR_GEOMETRY='MultiGeometry' &lt;ouputfolder&gt; &lt;input kml&gt;   For an example, KML file which has MultiGeometry, you can see the us_states.kml hosted by Google.    Other info: I am using 'GDAL 1.10.1, released 2013/08/26' for windows. How to remove specific elements in a numpy array I have some files that Ubuntu can't read it ( ANSI encoding ) but Windows can read it well.  When I open it in gedit or notepad++ it seems like this :     Êã ÇáÊÍæíá áÜÜ   How can I make Ubuntu read ANSI encoded files well? Definition of complex number In many situations (problems as well as solutions) I encounter the complex number $i$ which many times is defined as $i^2=-1$ instead of $i=\sqrt{-1}$, since it is "more preferred". Does anyone know why? Is it because there are two solutions to the equation $x^2+a=0, \ \ a&gt;0$? The difference between two periodic functions converges to zero, is this two functions identical?