Prove that (Log A)2 - (Log B)2 = Log ( a B ) . Log ( Ab ) - Mathematics

Prove that (log a)² - (log b)² = `"log"("a"/"b")."log"("ab")`

Sum

L.H.S.
= (log a)² - (log b)²
= (log a + log b)(log a - log b) ...{using identity m² - n² = (m + n)(m - n)}
= `"log"("ab")"log"("a"/"b")`

= `"log"("a"/"b")."log"("ab")`
= R.H.S.

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