Question

If m²+n²=17mn, then show that 2log(m-n) = log 15 + log m + log n.

Answer 1

L.H.S= m²+n² = 17mn

R.H.S= 2log(m-n) = log 15 + log m + log n

Solving RHS,

Using log _a (b^c) = c log _a b

log (m-n)² = log 15 + log m + log n

Using log _a b + log _a c = log (ac)

log (m-n)² = log 15mn

(Log gets cancelled out)

(m-n)² = 15mn

Using (a-b)² = a²+b²-2ab

m²+n²-2mn = 15mn

m²+n² = 17mm

Proved since L.H.S = R.H.S

I solved it on my own, it was easier than I thought.