State, True Or False : Log X/Log Y = Log X - Log Y

State, true or false :
`log x/log y` = log x - log y

बेरीज

We know that
`log(m/n) = logm - logn`
∴ `log x/log y ≠ log x - log y`
Thus the statement, `log x/log y`= log x - log y is false.

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Laws of Logarithm

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पाठ 8: Logarithms - Exercise 8 (B) [पृष्ठ १०७]

पाठ 8 Logarithms
Exercise 8 (B) | Q 10.2 | पृष्ठ १०७

Express in terms of log 2 and log 3 : log 4.5

Express in terms of log 2 and log 3:

`log26/51 - log91/119`

Express the following in a form free from logarithm:
2 log x + 3 log y = log a

Evaluate the following without using tables :
log 4 + `1/3` log 125 - `1/5`log 32

Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `

Express log₁₀2 + 1 in the form of log₁₀x .

Solve for x : log (x² - 21) = 2.

If log 2 = 0.3010 and log 3 = 0.4771; find the value of:

`2/3` log 8

Solve for x :
`log 225/log15` = log x

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b' : log 5.4