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")`

बेरीज

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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More About Logarithm

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पाठ 10: Logarithms - Exercise 10.2

पाठ 10 Logarithms
Exercise 10.2 | Q 36

If x = log 0.6; y = log 1.25 and z = log 3 - 2 log 2, find the values of :
(i) x+y- z
(ii) 5^{x + y - z}

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

Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.

Evaluate: log_ba × log_c b × log_a c.

Evaluate: `(log_5 8)/(log_25 16 xx Log_100 10)`

Solve the following:
log(x²+ 36) - 2log x = 1

Express log₁₀3 + 1 in terms of log₁₀x.

Express the following in a form free from logarithm:
2 log x + 3 log y = log a

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