Formula and laws of logarithms

Product rule: log_{b}AC = log_{b}A + log_{b}C
 Ex: log_{4}64 = log_{4}4 + log_{4}16 = log_{4}(4•16)
 practice problems on the product rule

Quotient rule: log_{b}(A/C) = log_{b}A − log_{b}C

Ex: $$ log_3(\frac{27}{9}) = log_3(27)  log_3(9) = 32 =1 $$
practice problems on the quotient rule

Ex: $$ log_3(\frac{27}{9}) = log_3(27)  log_3(9) = 32 =1 $$

Power rule: log_{b}A^{C} = C(log_{b}A)
 Ex: log_{3}9² = 2log_{3}9
Practice problems on the power rule
 Ex: log_{3}9² = 2log_{3}9
Product Rule Practice Problems
log12 + log5 = log(12*5) = log60
log_{3}12 + log_{3}11 = log_{3}(12 *11) = log_{3}132
log_{5}11 + log_{5}a = log_{5}(11*a) = log_{5}11a
Quotient Rule Practice Problems
$ log20 log5 = log(\frac{20}{5}) = log4 $
$ log_2(100) log_2(25) = log_2(\frac{100}{25}) = log_2(4). $
log_{2}4 is a logarithm equation that you can solve and get an answer of 2
$ log_2(40)  log_2(5) = log_2(\frac{40}{5}) = log_2(8). $
log_{2}8 is a logarithm equation that you can solve and get an answer of 3
$ log_3(18)  log_3(2) = log_3(\frac{18}{2}) = log_3(9). $
log_{3}9 is a logarithm equation that you can solve and get an answer of 2
Power Rule Practice Problems
log_{3}x^{2}= 2log_{3}X
log_{3}9^{x}= xlog_{3}9
log_{3}9 can be solved as a logarithmic equation. log_{3}9 = 2Therefore, the final answer is x(2) or 2x
Practice Problems:
all rules and formulas
After applying these rule of logarithms , substitute in the value of log x and log y

Practice Problems:
 product rule practice
 quotient rule practice
 power rule practice