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Salvador Bush

Salvador Bush

Answered question

2022-07-04

If a ² + b ² = 7 a b where a and b are positive then show that l o g ( 1 / 3 ( a + b ) ) = 1 / 2 ( l o g a + l o g b )

Answer & Explanation

Karla Hull

Karla Hull

Beginner2022-07-05Added 20 answers

a 2 + b 2 = 7 a b follows ( a + b ) 2 = 9 a b or a + b = 3 ( a b ) 1 2 or 1 3 ( a + b ) = ( a b ) 1 2 . Thus
log 1 3 ( a + b ) = log ( a b ) 1 2 = 1 2 ( log a + log b ) .
Caleb Proctor

Caleb Proctor

Beginner2022-07-06Added 1 answers

HINT:
As a 2 + b 2 = ( a + b ) 2 2 a b , we have ( a + b ) 2 = 9 a b
Apply Sum of Logarithms formula ((2)

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