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

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

Sum

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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Chapter 8: Logarithms - Exercise 8 (B) [Page 107]

Chapter 8 Logarithms
Exercise 8 (B) | Q 10.2 | Page 107

Express in terms of log 2 and log 3 :
`"log"26/51 - "log"91/119`

Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`

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

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

Evaluate the following without using tables :
log 5 + log 8 - 2 log 2

Find x, if : x - log 48 + 3 log 2 = `1/3`log 125 - log 3.

Solve for x : log (x - 2) + log (x + 2) = log 5

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`

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

State, true or false :
If `log 25/log 5 = log x`, then x = 2.