Question

Calcula los siguientes logaritmos:a)log 0,001 10b)log 9 3c)log 0,25 2d)log 2 2 .

Answer 1

a.)
${0,001= \frac{1}{1000}}\\\\{\log \left(\frac{1}{1000}\right)=x}\\\\{10^{\log \left(\frac{1}{1000}\right)} =10^x}\\\\{\frac{1}{1000}=10^x}\\\\{10^{-3}=10^x}\\\\{x=-3}$


b.)
${\log _9 (3) =x} \\\\{9^{\log_9 (3) }=9^x}\\\\{3=9^x}\\\\{3 = 3^{2x}}\\\\{2x=1}\\\\{x=1/2}$


c.)
${\log_{\frac{1}{4} } (2) = x}\\\\\\{\dfrac{1}{4}^{\log_{\frac{1}{4}}(2)}= \dfrac{1}{4}^x}\\\\\\{2= 2^{-2x}}\\\\{x=-\frac{1}{2}}$


d.)
${\log_2 (2)=x}\\\\{2^{\log_2 (2)} =2^x}\\\\{2 = 2^x}\\\\{x=1}$


Salu2. :)