Question

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?

Answer 1

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) = $\frac{\log(y)}{\log(x)}$        (Here the log has same base in the numerator and the denominator i.e 10)

therefore,

log₂(3) =  $\frac{\log(3)}{\log(2)}$

also,

log(2) = 0.3010

log(3) = 0.4771

thus,

log₂(3) =  $\frac{0.4771}{0.3010}$

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