To evaluate log2(3), Autumn reasoned that since log2(2) = 1 and log2(4) = 2, log2(3) must be the average of 1 and 2 and therefore log2(3) = 1.5. Use the definition of logarithm to show that log2(3) cannot be 1.5. Why is her thinking not valid?
Accepted Solution
A:
Answer:log₂(3) = 1.585 ≠ 1.5Her thinking is not valid because the technique of average is valid only if the graph of the function is a straight line, but the graph of the log function is not a straight line.Therefore the values cannot be taken by averageStep-by-step explanation:Given:log₂(2) = 1 log₂(4) = 2To evaluate : log₂(3)Now, we know thatlogₓ(y) = [tex]\frac{\log(y)}{\log(x)}[/tex] (Here the log has same base in the numerator and the denominator i.e 10)therefore, log₂(3) = [tex]\frac{\log(3)}{\log(2)}[/tex] also,log(2) = 0.3010log(3) = 0.4771thus, log₂(3) = [tex]\frac{0.4771}{0.3010}[/tex] orlog₂(3) = 1.585 ≠ 1.5Her thinking is not valid because the technique of average is valid only if the graph of the function is a straight line, but the graph of the log function is not a straight line.Therefore the values cannot be taken by average