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

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Question 249764:
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!

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

Answer by solver91311(24713) (Show Source):
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