Logb A X Logc B X Loga C

Evaluate: log_ba × log_c b × log_a c.

Sum

log_ba x log_c b x log_a c

⇒ ` ( log_10a)/ ( log _10b) ` x ` ( log_10b)/ ( log _10c ) ` x ` ( log_10c)/ ( log _10a) `

⇒ 1.

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Chapter 8: Logarithms - Exercise 8 (D) [Page 111]

Chapter 8 Logarithms
Exercise 8 (D) | Q 19.1 | Page 111

Evaluate :`1/( log_a bc + 1) + 1/(log_b ca + 1) + 1/ ( log_c ab + 1 )`

Given log₁₀x = 2a and log₁₀y = `b/2. "If" log_10^p = 3a - 2b`, express P in terms of x and y.

Solve : log₅( x + 1 ) - 1 = 1 + log₅( x - 1 ).

Solve for x, `log_x^(15√5) = 2 - log_x^(3√5)`.

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log ( x + 1) + log ( x - 1) = log 11 + 2 log 3

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

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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 log ₁₀125 = 3 (1 - log ₁₀ 2)

Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1