If Log1025 = X and Log1027 = Y; Evaluate Without Using Logarithmic Tables, in Terms of X and Y: Log103

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀3

योग

log₁₀27 = y
⇒ log₁₀3³ = y
⇒ 3log₁₀3 = y
⇒ log₁₀3 = `y/(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 18.2

If 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.

Express the following in terms of log 2 and log 3: log 648

Write the logarithmic equation for:

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

Express the following as a single logarithm:

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

Express the following as a single logarithm:

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

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

Simplify the following:

`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

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