Express the Following in Terms of Log 2 and Log 3: Log 144

Express the following in terms of log 2 and log 3: log 144

बेरीज

log 144
= log (2⁴ x 3²)
= log 2⁴ + log3²
= 4 log 2 + 2 log 3.

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Expansion of Expressions with the Help of Laws of Logarithm

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पाठ 10: Logarithms - Exercise 10.2

पाठ 10 Logarithms
Exercise 10.2 | Q 1.3

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

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

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

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Write the logarithmic equation for:

V = `(1)/("D"l) sqrt("T"/(pi"r")`

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

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 log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

Find the value of:

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