Logarithms Worksheet Page 2
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2Common logarithm and natural logarithm
Two logarithms receive special attention:
base 10 logarithm. This is the most popular logarithm and it is also called common logarithm.
log
log
It can be shown as
, but it is more often shown as just
10
base e logarithm. This is also called natural logarithm. It can be shown as
log
, but it is more
e
ln
often shown as
These two logarithms can be evaluated using a calculator.
Use a calculator to evaluate each logarithm. Round your answers to the nearest thousandth.
log
100
ln
18
log
20
ln
2
log
2
ln
e
Rewriting to solve equations
Equations involving logarithms can often be solved by rewriting them in exponential form. The
equivalent exponential equation is often easy to solve!
Solve each equation by rewriting it first in exponential form:
log
x
4
log 81 2
x
3
(Hint: remember that logarithms must have a positive
base)
x
log
2
log 0.001
3
11
x
x
6log
5 8
2log 64
5 7
x
16
(Hint: before rewriting in exponential form, you must solve
for the logarithm, leaving it by itself on one side of the
equation)
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