Step 3:
0.03
ln 2
0.
ln
1
03
ln 2
0.03
e
t
t
=
⋅
=
0.03
t
0.03
ln 2
ln 2
0.03
t
=
=
Hint: Use your calculator to numerically evaluate your expression for
x
, and round your answer
to the nearest millionth.
Answer:
ln 2
0.6931471806
0.03
0.0
23.104906
3
02
23.104906
t
t
=
≅
≅
≅
Example D
Solve:
2
1
3
3
10
x
x
−
−
=
.
Express your answer exactly, in terms of logs, and also give a numerical
approximation, accurate to the nearest millionth.
Taking the natural log of both sides of the equation, we get:
(
)
(
)
2
1
3
2
1
3
3
10
3
1
ln
0
ln
x
x
x
x
−
−
−
−
=
=
Now we can use the power rule, Property VI
, once on each side of the equation, to pull down the
exponents:
(
)
(
)
(
)
(
)
2
3
1
2
ln 3
ln 10
ln 3
l
0
3
n
1
1
x
x
x
x
−
−
−
−
=
=
Next we’ll solve for
x
. We start by using the distributive property to distribute the logs on each
side of the equation:
(
)
(
)
ln3
ln3
ln10
ln10
ln10
ln3
2
1
3
2
3
x
x
x
x
−
=
−
−
=
−
continued…