Logarithmic Equation: Simplifying with Easy Quick Method

[Slicktacker]

Does
$$(\log_{x}a - \log_{x}b - \log_{x}c) = \log_{x}(\frac{a}{b/c})$$?

 

[chroot]

No, it equals

$$\log_{x}(\frac{a}{b \cdot c})$$

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

- Warren

 

[chroot]

An easy way to remember this is to remind yourself of the log rule:

$$\log_x a^{-1} = - \log_x a$$

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:

$$a \cdot b^{-1} \cdot c^{-1} = \frac{a}{b \cdot c}$$

- Warren

 

[HallsofIvy]

$$\log_{x}(\frac{a}{b/c})$$
would be
$$(\log_{x}a - (\log_{x}b - \log_{x}c))$$

see the difference?