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 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

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

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Simplify : log (a)³ - log a

Simplify : log (a)³÷ log a

Express the following in terms of log 5 and/or log 2: log160

Write the logarithmic equation for:

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

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 log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45