If Log X = a + B and Log Y = A-b, Express the Value of Log X 2 10 Y in Terms of a and B.

If log x = A + B and log y = A-B, express the value of `"log" x^2/(10y)` in terms of A and B.

बेरीज

`"log" x^2/(10y)`
= logx² - log10y
= 2logx - (log10 + logy)
= 2logx - logy - 1
= 2(A + B) - (A - B) -1
= A + 3B - 1.

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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 14

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.
Express 3^{2x - 3} in terms of m.

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 54

Express the following in terms of log 2 and log 3: log 144

Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

Express the following as a single logarithm:

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

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

If log 27 = 1.431, find the value of the following: log 9