Which option best describes how to show that the Product Rule of Logarithms works for the base 4 expression log 4 16 + log 4 4 ?
Responses
Evaluate both log 4 16 and log 4 4 and show that their product is equal to the value of log 4 64. - incorrect
Evaluate both log 4 16 and log 4 4 and show that their sum is equal to the value of log 4 64. - correct
Evaluate both log 4 16 and log 4 4 and show that their sum is equal to the value of log 4 20. - incorrect
Evaluate both log 4 16 and log 4 4 and show that their product is equal to the value of log 4 20. - incorrect
explain how you get the correct answer
The correct answer is: Evaluate both log 4 16 and log 4 4 and show that their sum is equal to the value of log 4 64.
To show that the Product Rule of Logarithms works, we can evaluate log4 16 and log4 4 separately.
log4 16 = 2 because 4^2 = 16
log4 4 = 1 because 4^1 = 4
Then, using the Product Rule of Logarithms (log a + log b = log a*b), we can add the two individual results:
log4 16 + log4 4 = 2 + 1 = 3
Finally, we can show that the sum of log4 16 and log4 4 is equal to the logarithm of the product of 16 and 4:
log4 64 = 3
Therefore, we have demonstrated that the Product Rule of Logarithms works for the base 4 expression log4 16 + log4 4.