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

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 144

Express in terms of log 2 and log 3:

`log26/51 - log91/119`

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

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

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

Express log₁₀2 + 1 in the form of log₁₀x .

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

Solve for x : ` ( log 128) / ( log 32 ) ` = x

Solve for x : ` (log 64)/(log 8)` = log x

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' : log `3 1/8`