Product of logarithms, prove this identity.2\log(a)\log(b)=\log(ab)^2−\log(a)^2−\log(b)2for a>1 and b>1?

zgribestika

zgribestika

Answered question

2022-01-21

Product of logarithms, prove this identity.

2log(a)log(b)=log(ab)2log(a)2log(b)2​​​​​​​

for a>1and b>1?

Answer & Explanation

Maria Lopez

Maria Lopez

Beginner2022-01-21Added 32 answers

(logab)2=(loga+logb)2
=(loga)2+(logb)2+2logalogb
Now, just rearrange by leaving 2logalogb on the right hand side.
Janet Young

Janet Young

Beginner2022-01-22Added 32 answers

Here's a hint: A2+2AB+B2=(A+B)2. Here's another hint: loga+logb=log(ab).

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