Simplify : Log (A)3 ÷ Log a

Simplify : log (a)³÷ log a

योग

log (a)³÷ log a
= 3 log a ÷ log a
= `(3 log a)/(log a)`
= 3

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Expansion of Expressions with the Help of Laws of Logarithm

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अध्याय 8: Logarithms - Exercise 8 (C) [पृष्ठ १०८]

अध्याय 8 Logarithms
Exercise 8 (C) | Q 6.2 | पृष्ठ १०८

Express the following in terms of log 2 and log 3: log 36

Express the following in terms of log 2 and log 3: log 54

Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Express the following as a single logarithm:

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

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀5

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log60

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

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

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)