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What are Logarithms?

Logarithms in base $a$

$2^3=$

$2^4=$

$3^4=$

$5^2=$

$7^3=$

$2^6=$

$4^0=$

$10^3=$

$10^5=$

$\Rightarrow \quad \log_2 8=$

$\Rightarrow \quad \log_2 16=$

$\Rightarrow \quad \log_3 81=$

$\Rightarrow \quad \log_5 25=$

$\Rightarrow \quad \log_7 343=$

$\Rightarrow \quad \log_2 64=$

$\Rightarrow \quad \log_4 1=$

$\Rightarrow \quad \log 1000=$

$\Rightarrow \quad \log 100000=$

Evaluate.

$\log _{4}64=$

$\log _{3}27=$

$\log _{4}4=$

$\log _{3}9=$

$\log _{4}256=$

$\log _{9}9=$

$\log _{5}125=$

$\log _{5}1=$

$\log _{2}1=$

$\log _{2}64=$

$\log _{5}25=$

$\log _{2}8=$

$\log _{7}343=$

$\log _{9}1=$

$\log _{7}7=$

$\log1000=$

$\log _{6}6=$

$\log _{2}4=$

$\log _{8}8=$

$\log _{3}81=$

$\log _{6}1=$

$\log _{2}32=$

$\log _{7}1=$

$\log _{9}81=$
Evaluate. Give your answers as fractions.

$7^{-2}$

$4^0$

$5^{-4}$

$3^{-5}$

$3^{-2}$

$2^{-2}$

$4^{-3}$

$8^{-1}$

Evaluate.

$\log _{4}\frac{1}{64}=$

$\log _{2}\frac{1}{16}=$

$\log _{6}\frac{1}{216}=$

$\log\frac{1}{1000}=$

$\log _{5}\frac{1}{125}=$

$\log _{2}\frac{1}{2}=$

$\log _{3}1=$

$\log _{2}\frac{1}{32}=$

$\log _{7}1=$

$\log _{5}1=$

$\log _{6}1=$

$\log _{2}\frac{1}{64}=$

$\log _{3}\frac{1}{243}=$

$\log _{7}\frac{1}{7}=$

$\log\frac{1}{10}=$

$\log\frac{1}{100}=$

$\log _{8}\frac{1}{8}=$

$\log _{5}\frac{1}{5}=$

Evaluate. Give your answers as fractions.

$16^{\frac{1}{2}}$

$16^{\frac{1}{4}}$

$81^{-\frac{1}{4}}$

$729^{-\frac{1}{3}}$

$1000^{-\frac{1}{3}}$

$625^{-\frac{1}{4}}$

$625^{\frac{1}{4}}$

$16^{-\frac{1}{4}}$

Evaluate. Give your answers as fractions.

$\log_{243}3$

$\log_{729}9$

$\log_{81}\frac{1}{3}$

$\log_{1000}10$

$\log_{16}2$

$\log_{100}10$

$\log_{729}\frac{1}{9}$

$\log_{25}\frac{1}{5}$

$\log_{16}\frac{1}{2}$

$\log_{32}\frac{1}{2}$

$\log_{25}5$

$\log_{64}8$

$\log_{625}5$

$\log_{16}4$

$\log_{512}\frac{1}{8}$

$\log_{81}3$

$\log_{27}3$

$\log_{243}\frac{1}{3}$