solving equations with powers Im trying to solve the equation 3*2^(−2/x)+2*9^(−1/x)=5*6^(−1/x) So far I tried applying logaritmas but it didnt prove helpful...are there any other ways?

Parker Pitts

Parker Pitts

Answered question

2022-09-06

solving equations with powers
Im trying to solve the equation
3 2 2 / x + 2 9 1 / x = 5 6 1 / x
So far I tried applying logaritmas but it didnt prove helpful...are there any other ways?

Answer & Explanation

Bestvinajw

Bestvinajw

Beginner2022-09-07Added 15 answers

Since 9 = 3 2 the equation becomes
3 × 2 2 / x + 2 × 3 2 / x = 5 × 2 1 / x 3 1 / x
so let a = 2 1 / x and b = 3 1 / x then we have
3 a ( a b ) + 2 b ( b a ) = 0 ( a b ) ( 3 a 2 b ) = 0
and since a b then 3 a 2 b = 0 hence
a 2 = b 3 2 1 / x 1 = 3 1 / x 1 ( 1 x + 1 ) ( ln 3 ln 2 ) = 0 x = 1
sengihantq

sengihantq

Beginner2022-09-08Added 3 answers

Set 2 1 x = a ,   3 1 x = b so the equation becomes 3 a 2 + 2 b 2 5 a b = 0

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