Logarithm: Rules, rules rules!
Rules and Formula of Logarithms
Formula and laws of logarithms
- Product rule: logbAC = logbA + logbC
- Quotient rule: logb(A/C) = logbA − logbC
- Ex: log3(27/9)= log327 − log39 = 3 − 2 = 2
Power rule: logbAC = C(logbA)
Product Rule Practice Problems
Worksheet on product rule of logarithms
Problem 1)
Rewrite log12 + log5 as a single term using the product rule formula
log12 + log5 = log(12*5) = log60
Problem 2)
Rewrite log 312 + log 311 using the product rule formula
log312 + log311 = log3(12 *11) = log3132
Problem 3)
Rewrite log 511 + log 5a using the product rule formula
log511 + log5a = log5(11*a) = log511a
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
log20 − log5 = log(20/5) = log4
Power Rule Practice Problems
worksheet on the power rule of logarithms
Practice problem 1) Rewrite log 3x 2 as a single term using the power rule formula
log3x2= 2log3X.
Practice Problems: all rules and formulas
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Scientifc Calculator With Log 
Now, apply the quotient rule and then the power rule
