State, True Or False : Log X X Log Y = Log X + Log Y

State, true or false :
log x x log y = log x + log y

Sum

We know that
logx + log y = logxy
∴ logx + log y ≠ logx x log y
Thus the statement logx + log y = logx 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 10.4 | Page 107

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

Solve for x : log₁₀ (x - 10) = 1

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

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 3.6

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

`2/3` log 8

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

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

Given that log x = m + n and log y = m - n, express the value of log ` ( 10x ) / ( y ^ 2 )` in terms of m and n.