Question

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

Answer 1

Step-by-step explanation:

Question

{ log( a + b ) = 1/2 (108

If

(loga + log b) then show that a = b.

Solution

log(a+b) = (loga + log b)

⇒ 2log (a+b) = log a + log b

2

⇒ log(a+b)² = log ab

⇒(a+b) ² = ab ⇒ (a + b)² = 4ab

⇒ (a + b)²-4ab=0⇒ (a - b)² = 0⇒a=b

$hope \: it \: helps \: you$

Answer 2

Step-by-step explanation:

log($\frac{a+b}{2}$)=$\frac{1}{2}$(log a+log b)  

=>log($\frac{a+b}{2}$)=$\frac{1}{2}$(log ab)

=>log($\frac{a+b}{2}$)=log√(ab)

=>$\frac{a+b}{2}$=√(ab)

=>a+b=2√(ab)

 

=>a²+b²+2ab=4ab

=>a²+b²−2ab=0

=>(a)²+(b)²−2(a)(b)=0

=>(a−b)²=0

=>a−b=0

=>a=b

Proved.

Hope it Helps You.