Question

prove that.. (log a)^2 - (log b)^2 = log a/b . log (ab)

Answer 1

LHS

( loga )² - ( logb )²

= ( log a - log b ) ( log a + log b )

= log a/b . logab

RHS

__________________________

→ what we have used: we used three formula in this sum

→ first formula is a² - b² = ( a - b ) ( a + b )

→ second and third formula is ↓

→ logx + logy = logxy

→ logx - logy = logx/y

Answer 2

We know that

(a+b) ( a - b) = a²-b²


(log a)^2 - (log b)^2

=(loga+logb) (loga-logb)

We know that log m + log n = log mn

log m - log n = log m/n

= log ab * log a/b.