16. Example
Using the quotient law,
write the given expression
as a single logarithm:
2
ln lnx x−
log(2 ) log( 1)x x− +
17. Try This
Using the quotient law, write
the given expression as a
single logarithm:
ln( 1) ln( 1)x x+ − −
1
ln
1
x
x
+
÷
−
18. Try This
Using the quotient law, write
the given expression as two
logarithms:
ln( 1) ln( 1)x x+ − −
1
ln
1
x
x
+
÷
−
19. Example
Using the power law, re-
write the given expression
and simplify if possible:
2
ln x 3log(2 )x
( 1)
ln( 1) x
x +
+ ( 1)ln( 1)x x+ +
20. Example
Using the power law, re-
write the given expression
and simplify if possible:
2
ln x 3log(2 )x
( 1)
ln( 1) x
x +
+ ( 1)ln( 1)x x+ +
21. Try This
Using the power law, re-
write the given expression
and simplify if possible:
2
log4
3
lne
5
log10
2log4
3ln 3e =
5log10 5=
22. Example
Use a combination of
logarithmic properties and
laws to re-write the given
expression:
2
2( 3)
ln
1
x
x
+
÷
−
23. Example
Use a combination of
logarithmic properties and
laws to re-write the given
expression:
3
10
log
1
x
x
÷
+
24. Try This
Use a
combination of
logarithmic
properties and
laws to re-
write the given
expression:
3
( 5)
ln
1
e x
x
−
÷
+
1 3ln( 5) ln( 1)x x+ − − +
25. Example
The 1989 world series
earthquake in San Francisco
measure 7.0 on the Richter
Scale. The great earthquake
of 1906 measured 8.3. How
much more intense was the
1906 quake?
( )0logR i i=
26. Example
Decibels are calculated by
the function where
is the minimum sound
intensity detectable by the
human ear. Find the decibel
level of a jet engine which is
10 billion times
010log( )i i
0i
0.i
27. Lesson Close
The manipulation of
logarithms is a fundamental
math skill that you will need
in upper level math courses
and in science and
engineering.