Product of logarithms, prove this identity. 2log(a)log(b)=log(ab)^2-log(a)^2-log(b)^2

Lyla Carson

Lyla Carson

Answered question

2022-09-23

Product of logarithms, prove this identity.
Is it hard to prove this identity:
2 log ( a ) log ( b ) = log ( a b ) 2 log ( a ) 2 log ( b ) 2
for a > 1 and b > 1?

Answer & Explanation

garnboernl

garnboernl

Beginner2022-09-24Added 8 answers

( log a b ) 2 = ( log a + log b ) 2 = ( log a ) 2 + ( log b ) 2 + 2 log a log b
Now, just rearrange by leaving 2 log a log b on the right hand side.
gemauert79

gemauert79

Beginner2022-09-25Added 2 answers

Here's a hint: A 2 + 2 A B + B 2 = ( A + B ) 2 . Here's another hint: log a + log b = log ( a b )

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