Express the Following in Terms of Log 5 And/Or Log 2: Log500

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

बेरीज

log500
= log (2² x 5³)
= log 2²+ log 5³
= 2 log 2 + 3 log 5.

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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 2.5

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

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

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Express the following in terms of log 2 and log 3: log 216

Express the following in terms of log 5 and/or log 2: log160

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Express the following as a single logarithm:

`2 + 1/2 "log" 9 - 2 "log" 5`

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

Simplify: log a² + log a^-1