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

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 the following in a form free from logarithm:

2 log x - log y = 1

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 4 + `1/3` log 125 - `1/5`log 32

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 25

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 12

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

If log₁₀ 8 = 0.90; find the value of : log₁₀ 4