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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.

$\log _{6}36=$

$\log _{8}1=$

$\log _{2}2=$

$\log10000=$

$\log _{4}4=$

$\log _{4}16=$

$\log _{9}9=$

$\log _{9}729=$

$\log _{6}216=$

$\log _{7}343=$

$\log _{5}5=$

$\log1000=$

$\log _{3}81=$

$\log _{3}3=$

$\log _{2}16=$

$\log _{2}8=$

$\log _{7}7=$

$\log _{3}27=$

$\log _{5}1=$

$\log _{7}1=$

$\log _{9}1=$

$\log100=$

$\log _{8}8=$

$\log _{5}125=$

Evaluate.

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

$\log _{8}1=$

$\log _{2}1=$

$\log _{5}\frac{1}{625}=$

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

$\log _{4}1=$

$\log _{4}\frac{1}{256}=$

$\log _{9}\frac{1}{9}=$

$\log _{9}\frac{1}{729}=$

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

$\log _{8}\frac{1}{64}=$

$\log _{9}1=$

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

$\log _{3}1=$

$\log _{8}\frac{1}{512}=$

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

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

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

Evaluate. Give your answers as fractions.

$\log_{16}4$

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

$\log_{1000}10$

$\log_{27}\frac{1}{3}$

$\log_{64}4$

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

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

$\log_{64}8$

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

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

$\log_{32}2$

$\log_{125}\frac{1}{5}$

$\log_{343}7$

$\log_{64}2$

$\log_{25}5$

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

$\log_{64}\frac{1}{4}$

$\log_{81}3$