WorksheetsNatural Logarithms
Total questions: 30
Worksheet time: 16mins
Name
Class
Date
1.
Find the value for x to the third decimal place: ln x = 5
a)
148.413
b)
13.591
c)
100000
d)
1.610
2.
Expand ln xy2z3
a)
6(lnx + lny - lnz)
b)
lnx + 2lny - 3lnz
c)
lnx + (1/2)lny + (1/3)lnz
d)
lnx + 2lny + 3lnz
3.
Solve the following equation for x. Round your solution to two decimal places.
ln3x + ln2x = 3
ln3x + ln2x = 3
a)
x = 12.91
b)
x = 4.02
c)
x = 3.35
d)
x = 1.83
4.
What is the value of ln(e7)
a)
2.718...
b)
1
c)
7
d)
Does not exist
5.
Solve for x:
5 e6x+3 = 0.1
5 e6x+3 = 0.1
a)
-1.152
b)
0.232
c)
-3.077
d)
-0.854
6.
Solve 5e3x - 2 + 15 = 35
a)
1.13
b)
1.29
c)
1.10
d)
0.87
7.
Simplify the following to a single natural logarithm;
ln(2x) + ln(y) - ln(z)
ln(2x) + ln(y) - ln(z)
a)
A
b)
B
c)
C
d)
D
8.
Solve the following equation. Round your answer to two decimal places;
5 ln(x) = 7
5 ln(x) = 7
a)
x = 4.06
b)
x = 2.04
c)
No solution
d)
None of the above
9.
Which of the following is the value of x given;
e^(x + 6) = 12
e^(x + 6) = 12
a)
x = ln 6
b)
x = -6 + ln12
c)
x = ln72
d)
x = ln(-2)
10.
Simplify eln(x)
a)
0
b)
1
c)
x
d)
8
11.
Rewrite in exponential form:
ln(2) = x
ln(2) = x
a)
2x = 10
b)
102 = x
c)
ex = 2
d)
e2 = x
12.
What is the log form of a = ey ?
a)
ln(a) = y
b)
ln(y) = a
c)
log(a) = y
d)
log(y) = a
13.
Log with a base "e" (loge) is the same thing as...
a)
"e"
b)
Natural Logarithm (LN)
c)
Common Logarithm (Log)
d)
Natural Log, base "e"
LNe
LNe
14.
Evaluate
a)
ln 8
b)
2
c)
4
d)
8
15.
Solve the following equation. Round your answer to two decimal places;
5 ln(x) = 7
5 ln(x) = 7
a)
x = 4.06
b)
x = 2.04
c)
No solution
d)
None of the above
16.
Solve the following equation. Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12
4 - 3 ln(2x + 10) = 12
a)
x = 2.20
b)
x = 1.68
c)
x = -5.00
d)
x = -4.97
17.
Solve the following equation for x. Round your solution to two decimal places.
ln3x + ln2x = 3
ln3x + ln2x = 3
a)
x = 12.91
b)
x = 4.02
c)
x = 3.35
d)
x = 1.83
18.
Solve the following equation for x. Round your solution to two decimal places.
ln2x - ln41 = 2
ln2x - ln41 = 2
a)
x = 0.36
b)
x = 151.48
c)
x = 41
d)
None of these are solutions
19.
Which of the following is the value of x given;
e(x+6) = 12
e(x+6) = 12
a)
x = ln 6
b)
x = -6 + ln12
c)
x = ln72
d)
x = ln(-2)
20.
Which of the following is the value of x given;
7e(3x-5) = 49
7e(3x-5) = 49
a)
x = 2.315
b)
x = 0.681
c)
x = 2.964
d)
No Solution
21.
To two decimal places, find the value of x given;
e(x+6) - 5 = 1
e(x+6) - 5 = 1
a)
There is no solution for x
b)
x = 408.43
c)
x = -4.21
d)
x = 248.72
22.
The natural logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
23.
Solve for x:
5 e6x+3 = 0.1
5 e6x+3 = 0.1
a)
-1.152
b)
0.232
c)
-3.077
d)
-0.854
24.
Condense
a)
A
b)
B
c)
C
d)
D
25.
Condense
a)
A
b)
B
c)
C
d)
D
26.
Solve.
a)
A
b)
B
c)
C
d)
D
27.
Solve for x:
e2x = 11
e2x = 11
a)
x = (LN 11)/2
b)
x = 2loge11
c)
x = 2eLOG 11
d)
x = LN (11/2)
28.
Solve the following equation. Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12
4 - 3 ln(2x + 10) = 12
a)
x = 2.20
b)
x = 1.68
c)
x = -5.00
d)
x = -4.97
29.
Solve: ln(4-v) = ln(3v)
a)
1
b)
-2
c)
No Solution
d)
-5
30.
Solve the following equation. Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12
4 - 3 ln(2x + 10) = 12
a)
x = 2.20
b)
x = 1.68
c)
x = -5.00
d)
x = -4.97
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