Write the Logarithmic Equation For: E = 1 2 M V 2 - Mathematics

Write the logarithmic equation for:

E = `(1)/(2)"m v"^2`

योग

E = `(1)/(2)"m v"^2`
Considering log on both the sides, we get

logE = `"log"(1/2 "m v"^2)`

= `"log"(1)/(2) + "log" "m" + "log" "v"^2`
= log1 - log2 + logm + 2logv
= logm + 2logv - log2.

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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 4.2

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

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

Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.

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

Express the following in terms of log 2 and log 3: log12⁸

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: `"log"2(1)/(4)`

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

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

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`