Question

va rog ajutati ma, multumesc!!!!

Answer 1

$\it =log_{100}\bigg(\dfrac{1}{\not2}\cdot\dfrac{\not2}{\not3}\cdot\dfrac{\not3}{\not4}\cdot\ ...\ \cdot\dfrac{\not99}{100}\bigg)=log_{100}\dfrac{1}{100}=log_{100}100^{-1}=-1$

Answer 2

$\displaystyle \underbrace{log_{100}\frac{1}{2} +log_{100}\frac{2}{3} +...+log_{100}\frac{99}{100} }=log_{100}\Bigg(\frac{1}{\not2} \cdot \frac{\not2}{\not3} \cdot \frac{\not3}{\not4} \cdot ...\cdot \frac{\not98}{\not99}\cdot \frac{\not 99}{100}\Bigg)= \\\\ ~~~~~~~~~~\boxed{log_ax+log_ay=log_axy}\\\\ =log_{100}\frac{1}{100} =\underbrace{log_{100}100^{-1}}=(-1)\cdot \underbrace{log_{100}100}=(-1) \cdot 1=-1\\~~~~~~~~~~~~~~~~~\boxed{log_ax^n=nlog_ax}~~~~~~~\boxed{log_aa=1}$