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 \ =\ -42)
and 
so:
(u\ -\ 36)\ =\ 0)
Replacing 
(6^x\ -\ 36)\ =\ 0)
Hence:
\ =\ \log_6(6))
Recalling:
\ =\ n\log_b(x))
And
\ =\ 1)
We can write
\ =\ \log_6(6))
Similarly:
\ =\ \log_6(36))
And noting that 
\ =\ 2\log_6(6))
and finally:
John
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