N 11-1
Evaluating Logarithms With a Calculator
Every Logarithm has a base (b)… logb x. Your calculator does two specific
bases, b = 10 and b = e (Euler’s number … e ≈ 2.718).
Base 10 is called the common logarithm and the 10 is usually not written.
So “log10 x” is written as “log x”. This is the LOG button on your calculator.
Base e is called the natural logarithm and this logarithm is written a different
way as well.
“loge x” is written as “ln x”. This is the LN button on your calculator.
Use the calculator to evaluate the following logarithms and powers.
Round to four decimal places (ten-thousandths) where necessary.
1. log 45 = __________
2. log 589 = __________
3. log 45,765 = __________
4. log 0.566 = _________
5. ln 45 = __________
6. ln 589 = __________
7. ln 45,765 = __________
8. ln 0.566 = _________
*What is 101.6532 ? ________
*What is e3.8067 ? ________
*What is 102.7701 ? ________
*What is e6.3784 ? ________
*What is 104.6605 ? ________
*What is e10.7313 ? ________
*What is 10–0.2472 ? ________
*What is e–0.5692 ? ________
N 11-1
There is a formula for changing the bases of logarithms. A logarithm is
equal to the division of two logarithms in the different base. The log of
the original base is in the denominator. Since our calculators do base10,
we usually change to common log to evaluate.
Change-of-base formula: log a x 
log b x log x

log b a log a
Use the change-of-base formula to evaluate the following to 4 decimal
places.
9. log225 = ___________
10. log512 = ___________
11. log0.55 = ___________
12. log2(-4) = ___________
13. log3 (0.677) = ___________
14. What would “log4(x)” look like in base 2? ___________