Simplify: Log B ÷ Log B2 - Mathematics

Simplify: log b ÷ log b²

बेरीज

log b ÷ log b²
= log b ÷ 2log b
= `("log" "b")/(2"log" "b")`

= `(1)/(2)`.

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Expansion of Expressions with the Help of Laws of Logarithm

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पाठ 10: Logarithms - Exercise 10.2

पाठ 10 Logarithms
Exercise 10.2 | Q 31.2

If 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Express the following in terms of log 5 and/or log 2: log20

Express the following in terms of log 5 and/or log 2: log500

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Simplify the following:

`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`