Given 10^0.69897 = 5, find log 500

Answer 1

Given 10^0.69897=5 (this is a close approximation), if we multiply both sides by 100 we will be in a position to determine the log 500. Since 100 = 10², the multiplication looks like this:

10²10^0.69897=5(100)

One the left since we are multiplying powers with the same base the exponents can be added:

10^2.69897=500

By inspection it is apparent that the exponent that you apply to a base of 10 to produce 500 is 2.69897.

If that is not so easy to see try taking the log of both sides:

log 10^2.69897= log 500

2.69897 log 10 = log 500 (power property of logarithms)

2.69897 (1) = log 500 (log 10 = 1)