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.

योग

`"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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अध्याय 10: Logarithms - Exercise 10.2

अध्याय 10 Logarithms
Exercise 10.2 | Q 13

If log (a + 1) = log (4a - 3) - log 3; find a.

Given: log₃ m = x and log₃n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Express the following in terms of log 5 and/or log 2: log250

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

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)`

If 2 log x + 1 = 40, find: log 5x

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`