Question

if log (a+b/2) = 1/2 ( log a + log b) =a=b​

Answer 1

$Given \: that \\ </p><p> log (a+b)/2 = 1/2 ( log a + log b) \\ </p><p> = > log (a+b)/2 = 1/2 log ab \\ </p><p> = > log (a+b)/2 = log √ab \\ </p><p> = > (a + b)² = 4ab \\ </p><p> = > a²+ b² + 2ab = 4ab \\ </p><p> = > a² + b² + 2ab - 4ab = 0 \\ </p><p> = > a² + b² - 2ab = 0 \\ </p><p> = > (a - b)² = 0 \\ </p><p> = > a - b = 0 \\ </p><p> = > a = b \\ \: hence \: proved$

Answer 2

Answer:

log{(a+b)/2}=1/2 log(ab)

=log(ab)1/2

(a+b)/2= (ab)1/2

a+b=2(ab)1/2

(va)2 +(vb )2-2vavb=0

(va -vb)2=0

va-vb=0

va=vb

a=b

Step-by-step explanation: