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

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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Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 36

If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.

Show that : log_a m ÷ log_ab m + 1 + log _ab

If log₂(x + y) = log₃(x - y) = `log 25/log 0.2`, find the values of x and y.

Evaluate: log_ba × log_c b × log_a c.

Solve for x, if : log_x49 - log_x7 + log_x`1/343` + 2 = 0

Solve for x: `("log"81)/("log"9)` = x

Solve for x: `("log"1331)/("log"11)` = logx

Solve for x: `("log"289)/("log"17)` = logx

Express the following in a form free from logarithm:
`2"log" x + 1/2"log" y` = 1

Prove that: `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)` = 2