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?

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) =        (Here the log has same base in the numerator and the denominator i.e 10)

therefore,

log₂(3) =  

also,

log(2) = 0.3010

log(3) = 0.4771

thus,

log₂(3) =  

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

x>-1

Step-by-step explanation:

-2x+5<7

subtract 5

-2x<2

divide by -2, the sign changes

x>-1