Solve some unusual log/exponential equations I understand about log and exponential equations/funct

juanberrio8a

juanberrio8a

Answered question

2022-06-26

Solve some unusual log/exponential equations
I understand about log and exponential equations/functions, but I can't solve these (the numbers are just examples, of course):
4 x = x + 10
x x = 3
( 2 x + 3 x 2 ) x + 1 = ( x x 3 ) x 2
Are there specific algebraic steps that I can follow so that I solve them? Or, if not, what are the other means to find x in each?

Answer & Explanation

Raven Higgins

Raven Higgins

Beginner2022-06-27Added 17 answers

Start reading. The second problem is solved here. As for the first one, here it goes:
4 x = x + 10 | ( 1 ) 4 ( x + 10 ) 4 10 = ( x + 10 ) 4 ( x + 10 ) | ln 4
4 10 ln 4 = ( x + 10 ) ln 4 e ( x + 10 ) ln 4 ( x + 10 ) ln 4 = W ( 4 10 ln 4 )
x = W ( 4 10 ln 4 ) ln 4 10.
And similarly for the third.

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