SOLUTION: {{{6^(2x)-42*(6^x)+216=0}}}

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This is a quadratic in 6^x
Sub z for 6^x -->
(z - 6)*(z - 36) = 0
z = 6
z = 36
-----
Sub back:
6^x = 6
x = 1
------
6^x = 36
x = 2

You can put this solution on YOUR website!




Note that

Which means that the equation takes on the form of a quadratic with the function assuming the role of the independent variable.

Let represent , then:



Note that and so:



Replacing



Hence:







Recalling:



And



We can write





Similarly:







And noting that



and finally:



John