Free Printable Natural Log (ln)

1.

Expand: ln (ab)

a)

ln a - ln b

b)

ln a + ln b

c)

(ln a)(ln b)

d)

Not possible to expan

2.

Expand: $\ln\ a^x$

a)

$x\cdot\ln a$

b)

$a\cdot\ln x$

c)

(ln a)(ln x)

d)

Not possible to expand

3.

Expand: $\ln\frac{a}{b}$

a)

$\frac{\ln a}{\ln b}$

b)

ln a + ln b

c)

ln a - ln b

d)

Not possible to expand

4.

Expand: $\ln\frac{xy}{z}$

a)

ln x - ln y + ln z

b)

ln x + ln y - ln z

c)

$\frac{\ln x\cdot\ln y}{\ln z}$

d)

Cannot expand

5.

Expand: $\ln\left(x-1\right)^3$

a)

$3\ln x-3\ln1$

b)

$3\ln\left(x-1\right)$

c)

$\ln x^3-\ln1$

d)

Cannot be expanded

6.

Evaluate if possible: $\ln e^5$

a)

5

b)

e

c)

0

d)

Undefined

7.

ln x has a base of ____

a)

1

b)

e

c)

0

d)

10

8.

Evaluate: $e^{\ln3}$

a)

Undefined

b)

0

c)

3

d)

$e^3$

9.

Condense: $3\ln x\ +\ 4\ln3$

a)

$\ln\left(x^3+81\right)$

b)

$\ln\left(3x+81\right)$

c)

$\ln\left(81x^3\right)$

d)

$\ln\left(243x\right)$

10.

Solve the equation. Check for extraneous solutions.

$\ln\left(9x-7\right)=\ln\left(5x+33\right)$

a)

$x=2$

b)

$x=-2$

c)

$x=10$

d)

$x=-10$

11.

Solve the equation. Check for extraneous solutions.

$e^{\left(5-2p\right)}+2=4$

a)

$p=2.1534$

b)

$p=-4.3069$

c)

$p=0.6931$

d)

$p=2.8466$

12.

Solve the equation. Check for extraneous solutions.

$-2e^c+14=-6$

a)

$c=-2.3026$

b)

$c=2.9957$

c)

$c=31.0986$

d)

$c=2.3026$

13.

Solve the equation. Check for extraneous solutions.

$e^x=21$

a)

$x=3.0445$

b)

$x=5.6857$

c)

$x=1.7559$

d)

$x=-4.0431$

14.

Solve the equation. Check for extraneous solutions.

$4e^{3k}+1=85$

a)

$k=3.0445$

b)

$k=1.0148$

c)

$k=3.0445$

d)

$k=1.3863$

Natural Log (ln)

Total questions: 14

Worksheet time: 4hrs 30mins

Similar Resources on Wayground