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.

योग

`"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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अध्याय 10: Logarithms - Exercise 10.2

अध्याय 10 Logarithms
Exercise 10.2 | Q 14

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 15

Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.

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

Express the following in terms of log 2 and log 3: log12⁸

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

Write the logarithmic equation for:

V = `(4)/(3)pi"r"^3`

Simplify the following:

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

Simplify the following:

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

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540