Exam Review Logs, etc. 1!
page 1 of 6!
Alg II!
Name________________________
06-03-15
Give answers to 4 decimal places where appropriate.
Part I: Logarithms
Solve for x:
x
1.
5 2 = 20
2.
x
x
12⋅6 = 10
3.
log (64) = 4
x
4.
log (101) = x
3
5.
ln 2x = 5
( )
6.
log x + 3 + log 2 x − 3 − log 2(1) = 4
2
7.
ln x 3 − ln e 4 = 5
( ) ( )
8.
⎛ 5⎞
1
3
log 5 x 5 + log 5 ⎜ x 2 ⎟ = 3
2
5
⎝ ⎠
(
)
( )
(
)
Exam Review Logs, etc. 1!
page 2 of 6!
Alg II!
Name________________________
06-03-15
Write as a single log or number, with no coefficient before the log. Show any work.
9.
(log (b))(log (c ))(log (d ))
10.
2log 5(x)+ log 5( y) 6log 2 xy
+
log 5(a)
log 2 a2
11.
Suppose you invest $1000 at an annual rate of 8%.
2
a
b
3
c
( )
( )
a) Find the final balance after 10 years if the interest is compounded quarterly.
b) Find the final balance after 10 years if the interest is compounded continuously.
c) What interest rated, compounded annually, would yield the same amount as would 8% compounded
continuously as in part b?
Exam Review Logs, etc. 1!
page 3 of 6!
12.
Alg II!
Name________________________
06-03-15
⎧log b (a) = 0.861353,
⎪
Given: ⎨ log b (c) = −1,
,
⎪
and ab = 20
⎩
a) find
log (b)
a
b) find
( )
log b ac 2
c) find the values of a, b, and c.
13.
The pressure of the air in the Earth’s atmosphere decreases exponentially with altitude above sea level.
The pressure at the Earth’s surface, sea level, is about 14.7 pounds per square inch (psi) and the pressure at 2000
feet is approximately 13.5 psi.
a) Write the equation expressing pressure, p, in terms of altitude, a.
b) Human blood at body temperature will boil if the pressure is below 0.9 psi. At what altitude would your blood
start to boil if you were in an unpressurized airplane?
Exam Review Logs, etc. 1!
page 4 of 6!
14.
Given
(
)
Alg II!
( )
Name________________________
06-03-15
2
log 2 16a2 = 2log 3 3b and log 2(a) = log 3(b) , find the values of a and b.
3
log (10) = a , find the exact value (in terms of a ) of
125
a) log 125 (20)
b) log 10 (5)
17. Given that
Exam Review Logs, etc. 1!
page 5 of 6!
Alg II!
Name________________________
06-03-15
Part II: Exponents
Simplify:
(12x )
−1
1.
⎛
⎞
⎜⎝ 625x y ⎟⎠
2
3
1 1
⎛
⎞
3 6
25x
y
⎜⎝
⎟⎠
1
3
−1
−
1
2
2.
−1
3.
x −2
−1
⎛ 2⎞
−1
⎜⎝ x ⎟⎠ − 4
4.
1
⎛
3 3⎞
⎜⎝ 10x y ⎟⎠
( 30x y )
−2
−6
−2
n
3
49 ⋅ 343 ⋅7 n+1 − 49n+1
n
⎛ 1 ⎞2
7 ⋅7 ⋅ ⎜ ⎟
⎝ 49 ⎠
−2
3n
Exam Review Logs, etc. 1!
page 6 of 6!
Alg II!
Name________________________
06-03-15
Solve for x:
5.
( )
( )
4 2x
9 = 12 27 x
3
6.
2 2x
⋅5 = 250
5
7. Find the values of a, b, c:
⎛ 43 ⎞
⎛ 216 ⎞ ⎜ 81 ⎟ a
b
c
⎜⎝ 125 ⎟⎠ ⎜ − 3 ⎟ = 2 ⋅10 ⋅3
⎝ 25 2 ⎠
2
3
8. Find the equation of the exponential function g(x) passing through the points
(0, 4) and (3, 108).