Logarithm: Rules, rules rules!

Rules and Formula of Logarithms

Formula and laws of logarithms

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 log312 + log311 using the product rule formula

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

Problem 3

Rewrite log511 + log5a using the product rule formula

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

Quotient Rule Practice Problems

worksheet on the quotient rule of logarithms
Problem 1

Rewrite log20 − log5 as a single term using the quotient rule formula

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

Problem 2

Rewrite log2100− log225 as a single term using the quotient rule formula

$ 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

Problem 3

Rewrite log240− log25 as a single term using the quotient rule formula

$ 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

Problem 4

Rewrite log318− log32 as a single term using the quotient rule formula

$ 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

Worksheet on the power rule of logarithms
Problem 1

Rewrite log3x2 as a single term using the power rule formula

log3x2= 2log3X

Problem 2

Rewrite log39x as a single term using the power rule formula

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

Problem 1

If log x = 4 and log y =2 what is the numeric value of

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