Free Printable 6.8 Natural Logarithms Practice

1.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

2.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

3.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

4.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

5.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

6.

Solve the following equation. Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12

a)

x = 2.20

b)

x = 1.68

c)

x = -5.00

d)

x = -4.97

7.

Which of the following is the value of x given;
7e^(3x-5) = 49

a)

x = 2.315

b)

x = 0.681

c)

x = 2.964

d)

No Solution

8.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

9.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

10.

Write the equation in logarithmic form.
$e^{\left(x-9\right)}=74$

a)

$\ln\left(x-9\right)=74$

b)

$x-9=\ln74$

11.

Write the equation in exponential form.
$\ln53=x$

a)

$e^{53}=x$

b)

$e^x=53$

12.

Write the equation in exponential form.
$\ln87=x+4$

a)

$e^{\left(x+4\right)}=87$

b)

$e^{87}=x+4$

13.

Condense the expression as a single logarithm.

$\ln4+\ln3x$

a)

$\ln7x$

b)

$\ln\left(3x\right)^4$

c)

$\ln12x$

14.

Expand the logarithmic expression.

$\ln\left(\frac{m^5}{n^2}\right)^3$

a)

$\ln\left(\frac{m^{15}}{n^6}\right)$

b)

$15\cdot\ln m-6\cdot\ln n$

c)

$15\cdot\ln m+6\cdot\ln n$

d)

$\ln m^{15}-\ln n^6$

15.

Solve the following equation for x. Round your solution to two decimal places.
ln2x - ln41 = 2

a)

x = 0.36

b)

x = 151.48

c)

x = 41

d)

None of these are solutions

6.8 Natural Logarithms Practice

Total questions: 15

Worksheet time: 3570secs

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