Evaluate log (base 9) 27. Can someone explain this one for me so i could do some tasks on my own?
You would use some properties of the logarithm. First, \(log_927=log_{3^2}27=\frac{1}{2}log_327\). So, now you have \(log_327\) to calculate. It's \(log_33^3=3\), so the final result is \(\frac{1}{2}*3=\frac{3}{2}\)
Hope it helps.
\(log_927=log_93^3=3log_93=3log_9\sqrt9=3log_99^\frac{1}{2}\\\\=\frac{1}{2}\cdot3log_99=\frac{3}{2}\)