if a^2+4b^2=12ab then log(a+2b) is
Answers
a²+4b²=12ab
(a)²+(2b)²=12ab
(a+2b)²-4ab=12ab
(a+2b)²=16ab
Taking log on both the sides, we get
log[(a+2b)²]=log(16ab)
2log(a+2b)=log(16)+log(ab)
log(a+2b)=1/2[log(16)+log(ab)]
log(a+2b)=(1/2)[log(16)+log(a)+log(b)]
log(a+2b)=(1/2)[log(16)]+(1/2)[log(a)+log(b)]
log(a+2b)=(1/2)log(2)⁴+(1/2)[log(a)+log(b)]
log(a+2b)=(1/2)[4log(2)+log(a)+log(b)]
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 helps you..