Logarithm: Rules, rules rules!

Formula and laws of logarithms

• Product rule: log_bAC = log_bA + log_bC
  • Ex: log₄64 = log₄4 + log₄16 = log₄(4•16)
  • practice problems on the product rule

• Quotient rule: log_b(A/C) = log_bA − log_bC
  • Ex: $$ log_3(\frac{27}{9}) = log_3(27) - log_3(9) = 3-2 =1 $$
    • practice problems on the quotient rule

Power rule: log_bA^C = C(log_bA)

• Ex: log₃9² = 2log₃9
  • Practice problems on the power rule

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

Answer

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

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

Answer

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

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

Answer

log₅11 + log₅a = log₅(11*a) = log₅11a

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

Answer

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

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

Answer

$ 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

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

Answer

$ 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

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

Answer

$ 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

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

Answer

log₃x²= 2log₃X.

Practice problem 2)Rewrite log₃9^x as a single term using the power rule formula

Answer

log₃9^x= xlog₃9.

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

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

Practice Problem 1) If log x = 4 and log y =2 what is the numeric value of

Step 1

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

Answer

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