Question

Hey !!!

Solve this question !!!

refer to attachment ..

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#Be brainly

Answer 1

Given a^2 + 4b^2 = 12ab.

It can be written as,

a^2 - 12ab + 4b^2 = 0

a^2 + 4ab - 16ab + 4b^2 = 0

a^2 + 4ab + 4b^2 - 16ab = 0

a^2 + 4ab + 4b^2 = 16ab

(a + 2b)^2 = 16ab.

Apply log on both sides, we get

We know that log ab = loga + log b

log(a + 2b)^2 = log16 * ab

2log(a + 2b) = log 16 + log ab

2log(a + 2b) = log 16 + log a + log b

log(a + 2b) = (log 16 + log a + log b)/2

log(a + 2b) = (log (4^2) + log a + log b)/2

log(a + 2b) = (4log 2 + log a + log b)/2

log(a + 2b) = (4log 2/2) + (log a+log b)/2

log(a + 2b) = 2log 2 + (log a+ log b)/2


Hope this helps!

Answer 2

Hey there!

a² + 4b² = 12ab

Add-ing 4ab on both sides,

a² + 4ab + 4b² = 16ab

( a + 2b )² = 16ab

Now,
Applying logarithm on both sides,

log ( a + 2b )² = log ( 16ab )

2 log ( a + 2b ) = log 16 + log a + log b

log ( a + 2b ) =( log 16 + log a + log b) /2

log ( a + 2b ) = 4log2 / 2 + ( log a) + ( log b) / 2

log ( a + 2b ) = 2log2 + log √a + log √b

Hope helped!