If Log a = P and Log B = Q, Express a 3 B 2 in Terms of P and Q. - Mathematics

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

बेरीज

`"log" "a"^3/"b"^2`
= loga³ - logb²
= 3loga - 2logb
= 3p - 2q.

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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 13

If log₁₀ 8 = 0.90; find the value of : log 0.125

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

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

Write the logarithmic equation for:

n = `sqrt(("M"."g")/("m".l)`

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

If 2 log x + 1 = 40, find: x

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

If log 27 = 1.431, find the value of the following: log300