Question

log4 0,125+log0,5 32

Answer 1

$log_{ a^{n} } b= \frac{1}{n}* log_{a} b$
1. $log_{4} 0,125= log_{ 2^{2} } 0,125= \frac{1}{2}* log_{2}0,125= \frac{1}{2} * log_{2} \frac{125}{1000} = \frac{1}{2} * log_{2} \frac{1}{8} =$
$= \frac{1}{2}* log_{2} 2^{-3} = \frac{1}{2}*(-3)=-1,5$

2. $log_{0,5}32= log_{ \frac{1}{2} } 32= log_{ 2^{-1} } 32=(1:(-1))* log_{2}32=- log_{2} 2^{5} =-5$

3. -1,5+(-5)=-6,5