Free Printable Simplify Logs & Natural Logs

1.

Simplify: log 10⁵

a)

10

b)

5

c)

10

d)

can't be simplified

2.

Simplify: $2\ln5$

a)

can't be simplified

b)

$\ln10$

c)

$\ln7$

d)

$\ln5^2$

3.

Simplify: $\ln e$

a)

$e$

b)

$\ln1$

c)

$1$

d)

can't be simplified

4.

$\ln$ is

a)

a common log

b)

a natural log

c)

Euler's number

d)

the most simplified form of a log

5.

$\log_37$ is equivalent to

a)

$\frac{\log7}{\log3}$

b)

$\frac{\log3}{\log7}$

c)

$\log\left(3\cdot7\right)$

d)

$\log\left(\frac{7}{3}\right)$

6.

$\log_bb^x=b^{\log_bb^x}$

a)

Product Property

b)

Inverse Property

c)

Quotient Property

d)

Change of Base Rule

7.

$\log\left(m\cdot n\right)=\log m+\log n$

a)

Inverse Property

b)

Power Property

c)

Product Property

d)

Quotient Property

8.

$\log_bm=\frac{\log m}{\log b}$

a)

Quotient Property

b)

Change of Base Rule

c)

Product Property

d)

Inverse Property

9.

$k\cdot\log_bm=\log_bm^k$

a)

Power Property

b)

Quotient Property

c)

Inverse Property

d)

Product Property

10.

$\log\left(\frac{m}{n}\right)=\log m-\log n$

a)

Product Property

b)

Inverse Property

c)

Change of Base Rule

d)

Quotient Property

11.

Which of the following is true about $e$ ? (Choose two answers)

a)

It is called "Euler's number"

b)

It is the base in "log 3"

c)

Its value is exactly 2.718

d)

It is approximately 2.718

12.

$\log$ (represented without a base) is

a)

the base of $\ln$

b)

a natural log

c)

a common log

d)

not an exponent

13.

Condense into one log: $\log_52+\log_54+\log_54-\log_516$

a)

$\log_5\left(\frac{32}{16}\right)$

b)

$\log_5\left(-6\right)$

c)

$\log_52$

d)

can't be condensed

14.

Simplify: $5\cdot\log_232$

a)

can't be simplified

b)

32

c)

10

d)

25

15.

Convert into log form: $4^3=64$

a)

$\log_464=3$

b)

$\log_43=64$

c)

$3=3$

d)

$\ln4^3=64$

Simplify Logs & Natural Logs

Total questions: 15

Worksheet time: 8mins

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