Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places.
A) 20.09
B) 4.00
C) 64.00
D) 243.00
E) no solution

Question

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places.  ​
A) 20.09 
B) 4.00 
C) 64.00 
D) 243.00 
E) no solution

Quizplus · Accepted Answer

Using the properties of logarithms, we can simplify the expression as follows:
log(base 4)64 - log(base 4)16 + log(base 4)1/4
= 3 - 2 + (-2)
= -1

Now, we can use the change-of-base formula (logarithm base conversion formula) to check our answer:
log(base 4)1 = log(1)/log(4) ≈ -0.50

We can see that our answer is correct, rounded to two decimal places.

Use Properties of Logarithms or a Definition to Simplify the Expression