State, True Or False : Log 1 X Log 1000 = 0

State, true or false : log 1 x log 1000 = 0

Sum

We have,
log 1 = 0 and log 1000 = 3
∴ log 1 x log 1000 = 0 x 3 = 0
Thus the statement, log 1 x log 1000 = 0 is true.

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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 10.1 | Page 107

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 - log y = 1

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

Solve for x : log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3

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

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

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 60

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