Question

two students are trying to finish labeling the number line with the base 10 logarithmic expression that equal 2. Dylan say the missing logarithm should be log 505 because 505 is halfway between 10 and 1000, just like 2 is halfway between 1 and 3 . Jakob disagree. he says the miss logarithm should be log 100 . Which student is correct

Answer 1

Jakob is correct.

The base 10 logarithmic function is a continuous function, which means that the distance between any two consecutive values on the number line is the same. Therefore, if 2 is halfway between 1 and 3, the value of the logarithm that is halfway between log 1 and log 3 should be the average of log 1 and log 3, which is:

(log 1 + log 3) / 2 = (0 + 0.477) / 2 = 0.2385

To find the value of x such that 10^x = 505, we can take the logarithm of both sides using base 10:

log 10^x = log 505

x = log 505

Using a calculator, we can find that log 505 is approximately 2.702.

To find the value of x such that 10^x = 100, we can take the logarithm of both sides using base 10:

log 10^x = log 100

x = log 100

Using a calculator, we can find that log 100 is exactly 2.

Therefore, the logarithm that is equal to 2 is log 100, not log 505.