Question

if
${a}^{2} + 4b ^{2} = 12ab$
Then find log (a+2b)

Answer 1

Step-by-step explanation:

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

• I hope this help you..