Answer:
log₂(3) = 1.585 ≠ 1.5
Her 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
Step-by-step explanation:
Given:
log₂(2) = 1
log₂(4) = 2
To evaluate : log₂(3)
Now,
we know that
logₓ(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) = 0.3010
log(3) = 0.4771
thus,
log₂(3) = [tex]\frac{0.4771}{0.3010}[/tex]
or
log₂(3) = 1.585 ≠ 1.5
Her 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
