Download Review Sheet 5.3-5.4 Answer sheet

Name:_____________________________Date:____________________________
Trigonometry
5.3-5.4 Review Sheet
Evaluate the logarithm using the change of base formula. Round your answers to three
decimal places.
1.
2.
3.
4.
5.
log3 12
log2 60
log9 2
log3 57
2log5 15
5.907
2.262
.315
3.365
3.680
Use the properties of logarithms to write the expression as a sum, difference, and/or multiple
of logarithms.
6.
7.
8.
xy2
6
2
ln xyz
log2
log5 2
5
z
x + 1
ln x + ln y + 2 ln z
9.
1/ ln
2
x + 2 ln y - 5 ln z log5 6 – 1/2log5(x2 + 1)
10.
3
ln
log4 5x y
log4 5 + 3log4 x + log4 y
1/ 3ln
2
x3y2
z
15.
ln x – 4 ln(x + 2) + ln (x – 2)
ln
x
(x+2)4(x – 2)4
log6
x + 2 ln y - ln z
Write the expression as the logarithm of a single quantity.
12.
13.
ln y + 5 ln t
2 log2 (x + 4)
ln yt5
11.
– 3log6 z
14.
log x – 2 log y + 3 log z
3
log xz2
y
log2 (x + 4)2
16.
1
z3
17.
2 log5 8 + 5 log5 (z – 4)
1
log3 5x
4
log5 64(z - 4)5
log3 4 5x
Solve the following transcendental equations. Round your solutions to three decimal places.
18.
19.
2
2x
x
–
2x
e =e
4ex = 91
91
x = ln 4  3.125
x=0&x=4
20.
21.
4-3t
32x = 80
= .10
t = -1 log4 0.1  .554
3
22.
x = 1 log3 80  1.994
2
23.
4
2x – 7
8(46 – 2x )+ 13 = 41
= 64
x = -1 log4 7/2 + 3  2.548
2
x=5
24.
25.
ln x = -3
log 3z = 2
z = 100/3  33.333
x = e-3  .050
26.
27.
2 – 6 ln x = 10
x = e-4/3  .264
28.
ln x + ln(x + 3) = 1
-3 - 9 + 4e
x = -3 + 9 + 4e & x =
2
2
29.
log (x – 6) = log (2x + 1)
x = -7 No Solution
log2 x + log2 (x + 2) = log2 (x + 6)
x = 2 & x = -3