8.5: Properties of Logarithms
Algebra II
Let’s Play!
Ex. 1) If x
log 5 3 log 5 7
how can we combine these logarithms?
log 3 8 log 3 5
how can we combine these logarithms?
Note:
Ex. 2)
If x
Note:
Ex. 3)
If we are given log 12 x
4
how can we rewrite this without the exponent?
Note:
Ex. 4)
Note:
If 5
x
7 how do I solve for x?
“The dark side calls constantly for
aggression, revenge, betrayal. The stronger
you become, the more you're tempted."
Properties of Logarithms
1)
3)
2)
4)
NON-calculator examples
Use properties of logarithms to find the value of the expression.
For examples 5-9, you are given:
Ex 5.)
Ex 6.)
ln 6
Ex. 10)
log 4 32
ln 12 2.485
ln 24
and
ln 2 .693, find:
Ex 7.)
ln 144
Ex. 11)
Ex. 8)
Ex. 12)
log 27 9
Ex. 9) ln
ln 3
log 125
1
6
1
25
Expand the following.
6
Ex. 13) log 7 ( 2 x )
Ex. 15) ln
Ex. 14) log 2
5 x 4 y 10
a 9b 7 c 4
Ex. 16)
log 14
4x3
y
xy
3 ab
Condense the following.
Ex. 17) 2 log 3 x
Ex. 19) 2(log 3 x
4 log 3 y 7 log 3 z 2 log 3 r
4 log 3 y ) (7 log 3 z 2 log 3 r )
Ex. 18) 2 [log 7 x
4
Ex. 20) 2 [log 7 x
4
log 7 y ] 5[log 7 z 2
2 log 7 a 3 log 7 b]
log 7 y ] 5[log 7 z 2
2(log 7 a 3 log 7 b)]