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

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

Prove that : If a log b + b log a - 1 = 0, then b^a. a^b = 10

Simplify : log (a)³ - log a

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:

`(1)/(2)"log"25 - 2"log"3 + "log"36`

Simplify the following:

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

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)

Simplify: log b ÷ log b²