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# Logarithm: Rules, rules rules!

## Rules and Formula of Logarithms

### Formula and laws of logarithms

• Quotient rule: logb(A/C) = logbA − logbC
• Ex: $$log_3(\frac{27}{9}) = log_3(27) - log_3(9) = 3-2 =1$$
• Power rule: logbAC = C(logbA)
• Ex: log39² = 2log39
• ## Product Rule Practice Problems

Worksheet on product rule of logarithms

Problem 1) Rewrite log12 + log5 as a single term using the product rule formula

Problem 2) Rewrite log312 + log311 using the product rule formula

Problem 3) Rewrite log511 + log5a using the product rule formula

## Quotient Rule Practice Problems

worksheet on the quotient rule of logarithms

Practice problem 1) Rewrite log20 − log5 as a single term using the quotient rule formula

Practice problem 2) Rewrite log2100− log225 as a single term using the quotient rule formula

Practice problem 3) Rewrite log240− log25 as a single term using the quotient rule formula

Practice problem 4) Rewrite log318− log32 as a single term using the quotient rule formula

## Power Rule Practice Problems

worksheet on the power rule of logarithms

Practice problem 1) Rewrite log3x2 as a single term using the power rule formula