Question

if a^2+ b^2=23ab
show that
log a+b/5=1/2(log a+ log b)
​

Answer 1

log{(a + b)/5} = 1/2 (loga + logb)

Step-by-step explanation:

Given,

a² + b² = 23ab

or, a² + b² + 2ab = 23ab + 2ab

or, (a + b)² = 25ab

or, (a + b)² = 5² * a * b

Taking log to both sides, we get

log{(a + b)²} = log(5² * a * b)

or, 2 log(a + b) = log(5²) + loga + logb

or, 2 log(a + b) = 2 log5 + loga + logb

or, 2 {log(a + b) - log5} = loga + logb

or, 2 log{(a + b)/5} = loga + logb

or, log{(a + b)/5} = 1/2 (loga + logb)

Hence proved.