Logarithmic Equation: Simplifying with Easy Quick Method

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In summary, The expression in question is not equivalent to the provided log rule. The correct expression would be \log_{x}a - (\log_{x}b - \log_{x}c). This is because whenever there is a minus sign in front of a log, it should be converted to a plus sign and applied as a -1 exponent to the argument. Then, when adding the logs, the arguments should be multiplied.
  • #1
Slicktacker
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Does
[tex](\log_{x}a - \log_{x}b - \log_{x}c) = \log_{x}(\frac{a}{b/c})[/tex]?
 
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  • #2
No, it equals

[tex]\log_{x}(\frac{a}{b \cdot c})[/tex]

Perhaps you just made a mistake. [itex]a/b[/itex] divided by [itex]c[/itex] is [itex]a/(b \cdot c)[/itex].

- Warren
 
  • #3
An easy way to remember this is to remind yourself of the log rule:

[tex]\log_x a^{-1} = - \log_x a[/tex]

Whenever you see a minus sign in front of a log, mentally convert it to a plus sign and apply a -1 exponent to the argument. Then, when you add the logs, you multiply the arguments:

[tex]a \cdot b^{-1} \cdot c^{-1} = \frac{a}{b \cdot c}[/tex]

- Warren
 
  • #4
[tex] \log_{x}(\frac{a}{b/c})[/tex]
would be
[tex](\log_{x}a - (\log_{x}b - \log_{x}c)) [/tex]

see the difference?
 

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An "Easy quick log question" is a type of question that is designed to be simple and quick to answer, usually requiring only a few words or a short sentence. These types of questions are commonly used in surveys or quizzes to gather basic information or opinions from participants.

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