Question

Find the value of :
(i) ${\log }_{1/2}8$
(ii) ${\log }_{5}0.008$
(iii) ${\log }_{5}3125$
(iv) ${\log }_7\sqrt[3]{37}$

Answer 1

(i) ${\log }_{\frac{1}{2}}8={\log }_{\frac{1}{2}}{\left(\frac{1}{2}\right)}^{-3}=-3$

(ii) ${\log }_{5}0.008={\log }_5\frac{1}{125}={\log }_5{\left(5\right)}^{-3}=-3$

(iii) ${\log }_{5}3125={\log }_5{\left(5\right)}^5=5$

(iv) ${\log }_7\sqrt[3]{37}={\log }_7{\left(7\right)}^{1/3}=1/3$

Hence, this is the answer.