# Logarithm: Rules, rules rules!

Rules and Formula of Logarithms

### Product Rule Practice Problems

log12 + log5 = log(12*5) = log60

log312 + log311 = log3(12 *11) = log3132

log511 + log5a = log5(11*a) = log511a

### Quotient Rule Practice Problems

$log20 -log5 = log(\frac{20}{5}) = log4$

$log_2(100) -log_2(25) = log_2(\frac{100}{25}) = log_2(4).$

log24 is a logarithm equation that you can solve and get an answer of 2

$log_2(40) - log_2(5) = log_2(\frac{40}{5}) = log_2(8).$

log28 is a logarithm equation that you can solve and get an answer of 3

$log_3(18) - log_3(2) = log_3(\frac{18}{2}) = log_3(9).$

log39 is a logarithm equation that you can solve and get an answer of 2

### Power Rule Practice Problems

log3x2= 2log3X

log39x= xlog39

log39 can be solved as a logarithmic equation. log39 = 2

Therefore, the final answer is x(2) or 2x

### Practice Problems:all rules and formulas

Use the rules of logarithms to rewrite this expression in terms of logx and logy. Now, apply the quotient rule and then the power rule

After applying these rule of logarithms , substitute in the value of log x and log y

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