(31A) Logarithms in base a
$2^3$
$3^4$
$3^3$
$5^4$
$5^2$
$7^3$
$3^2$
$4^3$
$10^2$
$2^5$
$9^3$
$4^4$
$2^4$
$2^6$
$10^3$
$7^2$
$6^2$
$9^2$
$2^2$
$6^3$
$8^2$
$4^2$
$8^3$
$5^3$
Evaluate.
$\log _{4}4=$
$\log _{2}4=$
$\log _{5}125=$
$\log _{6}216=$
$\log _{4}1=$
$\log _{2}1=$
$\log _{3}1=$
$\log10000=$
$\log _{5}5=$
$\log _{3}9=$
$\log1000=$
$\log _{9}81=$
$\log _{2}16=$
$\log _{2}8=$
$\log100=$
$\log _{3}243=$
$\log _{8}1=$
$\log _{2}64=$
$\log _{8}8=$
$\log _{7}1=$
$\log _{7}343=$
$\log _{5}1=$
$\log _{6}6=$
$\log _{4}64=$
$\log _{3}3=$
$\log _{8}512=$
$\log _{7}7=$
$\log _{5}625=$
$\log _{8}64=$
$\log _{2}32=$
$\log _{3}81=$
$\log _{2}2=$
$\log _{9}9=$
$\log _{6}1=$
$\log _{4}256=$
$\log _{6}36=$
$\log _{3}27=$
$\log _{4}16=$
$\log _{7}49=$
$\log _{9}729=$
$\log _{5}25=$
$\log _{9}1=$
Evaluate. Give your answers as fractions.
$3^{-3}$
$3^{-5}$
$7^{-2}$
$4^{-3}$
$9^{-3}$
$8^{-3}$
$5^{-1}$
$5^{-4}$
$4^0$
$2^0$
$3^{-4}$
$8^{-1}$
$10^{-2}$
$4^{-1}$
$6^0$
$8^{-2}$
$6^{-2}$
$10^{-3}$
$10^{-1}$
$5^{-3}$
$4^{-4}$
$2^{-3}$
$9^{-1}$
$4^{-2}$
$7^{-1}$
$3^{-1}$
$2^{-1}$
$8^0$
$2^{-2}$
$7^0$
$3^{-2}$
$9^0$
$9^{-2}$
$2^{-4}$
$6^{-1}$
$5^0$
$6^{-3}$
$5^{-2}$
$3^0$
$7^{-3}$
$2^{-6}$
$2^{-5}$
Evaluate.
$\log _{8}1=$
$\log _{9}\frac{1}{729}=$
$\log _{3}\frac{1}{81}=$
$\log _{6}\frac{1}{36}=$
$\log _{3}\frac{1}{27}=$
$\log _{2}\frac{1}{64}=$
$\log _{8}\frac{1}{512}=$
$\log _{4}\frac{1}{256}=$
$\log _{3}\frac{1}{3}=$
$\log _{7}\frac{1}{49}=$
$\log _{4}\frac{1}{64}=$
$\log _{6}\frac{1}{6}=$
$\log _{5}1=$
$\log _{5}\frac{1}{25}=$
$\log _{7}\frac{1}{343}=$
$\log\frac{1}{100}=$
$\log1=$
$\log _{2}\frac{1}{8}=$
$\log\frac{1}{1000}=$
$\log _{2}1=$
$\log _{3}\frac{1}{9}=$
$\log _{8}\frac{1}{8}=$
$\log _{4}\frac{1}{4}=$
$\log _{7}1=$
$\log _{4}\frac{1}{16}=$
$\log _{8}\frac{1}{64}=$
$\log _{5}\frac{1}{5}=$
$\log _{9}1=$
$\log _{6}\frac{1}{216}=$
$\log _{7}\frac{1}{7}=$
$\log _{2}\frac{1}{16}=$
$\log _{9}\frac{1}{81}=$
$\log _{5}\frac{1}{125}=$
$\log _{5}\frac{1}{625}=$
$\log _{2}\frac{1}{32}=$
$\log _{4}1=$
$\log _{9}\frac{1}{9}=$
$\log _{2}\frac{1}{4}=$
$\log _{6}1=$
$\log _{2}\frac{1}{2}=$
$\log _{3}\frac{1}{243}=$
$\log\frac{1}{10}=$
Evaluate. Give your answers as fractions.
$8^{-\frac{1}{3}}$
$729^{-\frac{1}{3}}$
$16^{\frac{1}{4}}$
$729^{\frac{1}{3}}$
$4^{\frac{1}{2}}$
$100^{\frac{1}{2}}$
$25^{-\frac{1}{2}}$
$64^{-\frac{1}{2}}$
$625^{-\frac{1}{4}}$
$216^{-\frac{1}{3}}$
$81^{-\frac{1}{4}}$
$9^{\frac{1}{2}}$
$64^{\frac{1}{2}}$
$9^{-\frac{1}{2}}$
$8^{\frac{1}{3}}$
$64^{\frac{1}{6}}$
$625^{\frac{1}{4}}$
$36^{-\frac{1}{2}}$
$32^{-\frac{1}{5}}$
$243^{-\frac{1}{5}}$
$343^{\frac{1}{3}}$
$512^{-\frac{1}{3}}$
$125^{-\frac{1}{3}}$
$16^{\frac{1}{2}}$
$81^{\frac{1}{4}}$
$256^{\frac{1}{4}}$
$27^{\frac{1}{3}}$
$32^{\frac{1}{5}}$
$64^{\frac{1}{3}}$
$49^{\frac{1}{2}}$
$343^{-\frac{1}{3}}$
$256^{-\frac{1}{4}}$
$4^{-\frac{1}{2}}$
$1000^{\frac{1}{3}}$
$27^{-\frac{1}{3}}$
$512^{\frac{1}{3}}$
$16^{-\frac{1}{4}}$
$243^{\frac{1}{5}}$
$16^{-\frac{1}{2}}$
$81^{-\frac{1}{2}}$
$25^{\frac{1}{2}}$
$36^{\frac{1}{2}}$
$64^{-\frac{1}{3}}$
$125^{\frac{1}{3}}$
$100^{-\frac{1}{2}}$
$216^{\frac{1}{3}}$
$1000^{-\frac{1}{3}}$
$64^{-\frac{1}{6}}$
$49^{-\frac{1}{2}}$
$81^{\frac{1}{2}}$
Evaluate. Give your answers as fractions.
$\log_{256}4$
$\log_{16}\frac{1}{2}$
$\log_{343}7$
$\log_{729}9$
$\log_{64}\frac{1}{2}$
$\log_{343}\frac{1}{7}$
$\log_{216}6$
$\log_{64}8$
$\log_{243}\frac{1}{3}$
$\log_{81}9$
$\log_{81}\frac{1}{9}$
$\log_{49}\frac{1}{7}$
$\log_{27}\frac{1}{3}$
$\log_{125}\frac{1}{5}$
$\log_{32}2$
$\log_{36}\frac{1}{6}$
$\log_{16}\frac{1}{4}$
$\log_{64}\frac{1}{4}$
$\log_{81}3$
$\log_{625}5$
$\log_{8}\frac{1}{2}$
$\log_{27}3$
$\log_{4}2$
$\log_{512}\frac{1}{8}$
$\log_{25}5$
$\log_{36}6$
$\log_{16}4$
$\log_{64}\frac{1}{8}$
$\log_{16}2$
$\log_{81}\frac{1}{3}$
$\log_{625}\frac{1}{5}$
$\log_{64}2$
$\log_{216}\frac{1}{6}$
$\log_{512}8$
$\log_{4}\frac{1}{2}$
$\log_{9}\frac{1}{3}$
$\log_{100}10$
$\log_{9}3$
$\log_{32}\frac{1}{2}$
$\log_{64}4$
$\log_{256}\frac{1}{4}$
$\log_{125}5$
$\log_{8}2$
$\log_{1000}10$
$\log_{49}7$
$\log_{729}\frac{1}{9}$
$\log_{1000}\frac{1}{10}$
$\log_{243}3$
$\log_{25}\frac{1}{5}$
$\log_{100}\frac{1}{10}$