Lesson 8

Now, recall the basic rules for working with logarithms. For any real \(b, c>1\) and \(x,y>0\), the following properties hold:

• \(\log_{b}1 = 0\)


• \(\log_{b}b = 1\)


• \(\log_{b}(b^{x})=x\)


• \(b^{\log_{b}x}=x\)


• \(\log_{b}(xy)=\log_{b}x + \log_{b}y\)


• \(\log_{b}(x^{y})=y\log_{b}x\)


• \(\log_{b}\left(\frac{1}{y}\right)=-\log_{b}y\)


• \(\log_{b}\left(\frac{x}{y}\right)=\log_{b}x-\log_{b}y\)


• \(\log_{b} x = \frac{\log_c x}{\log_c b}\)

Problem. Compute \[\frac{\log_{2}{48}-2}{4+\log_{2}{9}}.\]