Question

If a⁴+ b⁴ = 14a²b² then show that log(a ²+b²) = loga + logb + 2log2,
(a, b>0)​

Answer 1

AnswEr:-

Here,

a⁴ + b⁴ = 14a²b²

or, (a²)² + (b²)² = 14a²b²

or, (a² + b²)² – 2a²b² = 14a²b²

or, (a² + b²)² = 16a²b²

Putting 'log' on both sides, we get,

or, log(a² + b²)² = log16a²b²

or, 2log(a² + b²) = log(4ab)²

or, 2log(a² + b²) = 2log(4ab)

or, log(a² + b²) = log4ab

or, log(a² + b²) = loga + logb + log4

or, log(a² + b²) = loga + logb + log2²

or, log(a² + b²) = loga + logb + 2log2

(Proved)

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Answer 2

If a⁴+b⁴=14a²b², then let us show that log(a²+b²)=log a+log b+2log 2

solving by- Rahbar Sabri