2. Simplify log,1000.
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Answer:
Rewrite
log
(
1000
)
=
x
log(1000)=x in exponential form using the definition of a logarithm. If
x
x and
b
b are positive real numbers and
b
b does not equal
1
1, then
log
b
(
x
)
=
y
logb(x)=y is equivalent to
b
y
=
x
by=x.
10
x
=
1000
10x=1000
Create equivalent expressions in the equation that all have equal bases.
10
x
=
10
3
10x=103
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
x
=
3
x=3
The variable
x
x is equal to
3
3.
3
3
l
o
g
(
1
0
0
0
)
log(1000)
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