Express the Following in Terms of Log 2 and Log 3: Log 36 - Mathematics

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

योग

log 36
= log (2 x 2 x 3 x 3)
= log (2² x 3²)
= log 2² + log 3²
= 2log 2 + 2log 3.

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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 1.1

Prove that : (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

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

Express the following in terms of log 5 and/or log 2: log80

Express the following in terms of log 5 and/or log 2: log125

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

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

`2 + 1/2 "log" 9 - 2 "log" 5`

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`