Logarithms: solve log(x + 2) - log(x - 1) = log 4

[Guest]

Use the laws of logarithms to solve the equation log(x + 2) - log(x - 1) = log 4.

 

[stapel]

Where are you stuck? You applied the log rule to the subtraction in order to combine the logs on the left-hand side and, once you had "log(something) = log(something else)", you equated the arguments, thus creating a rational equation. And... then what?

Please reply showing all of your work and reasoning. Thank you!

Eliz.

 

[skeeter]

Use the laws of logarithms to solve the equation log(x + 2) - log(x - 1) = log 4.

two rules for logs that you need (and should know) to solve this problem ...

1. \(\displaystyle \L \log(a) - \log(b) = \log\left(\frac{a}{b}\right)\)

2. If \(\displaystyle \L \log(c) = \log(d)\), then \(\displaystyle \L c = d\).