Free Printable Logarithm Properties Take-Home Formative

1.

Write the following equation in its equivalent exponential form.

$\log_2y=4$

a)

$2^4=y$

b)

$4^2=y$

c)

$y^2=4$

d)

$2^y=4$

2.

Write the following equation in its equivalent exponential form.

$\log10,000=4$

a)

$10^4=10,000$

b)

Not possible

c)

$e^4=10,000$

d)

$10,000^4=y$

3.

Write the following equation in its equivalent logarithmic form.

$2^a=b$

a)

$\log_2\left(a\right)=b$

b)

$\log_b\left(2\right)=a$

c)

$\log_2\left(b\right)=a$

4.

Write the following equation in its equivalent logarithmic form.

$5^4=625$

a)

$\log_54=625$

b)

$\log_5625=4$

c)

$\log_{625}5=4$

d)

$\log_{625}4=5$

5.

Evaluate the expression below without a calculator.

$\log_71=$

a)

0

b)

1

c)

-1

d)

Not possible

6.

Evaluate the expression below without a calculator.

$\ln\left(e\right)^{\frac{1}{3}}=$

a)

ln(e)

b)

$\frac{1}{3}\ln\left(e\right)$

c)

1/3

d)

1

7.

Evaluate the expression below without a calculator.

$\log_yy^4=$

a)

1

b)

y

c)

4

d)

0

8.

Evaluate the expression below without a calculator.

$\log_9\left(81\right)=$

a)

1

b)

2

c)

$\sqrt[]{81}$

d)

1/2

9.

Use the properties of logarithms to expand this logarithm as much as possible. Where possible, evaluate the expression without using a calculator.

$\log_2\left(\frac{8}{x^3}\right)=$

a)

$3-3\log_2\left(x\right)$

b)

$3+3\log_2\left(x\right)$

c)

$\log_2\left(8\right)-3\log_2\left(x\right)$

d)

$\log_2\left(8\right)+3\log_2\left(x\right)$

10.

Use the properties of logarithms to expand this logarithm as much as possible. Where possible, evaluate the expression without using a calculator.

$\log_5\left(25\cdot\sqrt[3]{x}\right)$

a)

$2+\frac{1}{3}\log_5\left(x\right)$

b)

$2-\frac{1}{3}\log_5\left(x\right)$

c)

$2+\log_5\left(\sqrt[3]{x}\right)$

d)

$\log_525+\log_5\left(\sqrt[3]{x}\right)$

11.

Use the properties of logarithms to expand this logarithm as much as possible. Where possible, evaluate the expression without using a calculator.

$\log_3\left(z\sqrt[]{xy}\right)$

a)

$\log_3\left(z\right)+\frac{1}{2}\log_3\left(x\right)+\frac{1}{2}\log_3\left(y\right)$

b)

$\log_3\left(z\right)+\frac{1}{2}\log_3\left(x\right)+\log_3\left(y\right)$

12.

Use the properties of logarithms to expand this logarithm as much as possible. Where possible, evaluate the expression without using a calculator.

$\log\left(\frac{u}{v^3}\right)^2$

a)

$2\log\left(u\right)-6\log\left(v\right)$

b)

$2\log\left(u\right)-3\log\left(v\right)$

13.

Use properties logarithms to condense the logarithmic expression as much as possible. Write the expression as a single logarithm whose coefficient is 1.

$\log_a\left(2\right)-\log_a\left(4\right)$

a)

$\log_a\left(\frac{2}{4}\right)$

b)

$\log_a\left(\frac{1}{2}\right)$

c)

$\log_a\left(8\right)$

14.

Use properties logarithms to condense the logarithmic expression as much as possible. Write the expression as a single logarithm whose coefficient is 1.

$3\log_2\left(3\right)-2\log_2\left(7\right)$

a)

$\log_2\left(\frac{27}{49}\right)$

b)

$\log_2\left(\frac{\sqrt[3]{3}}{\sqrt[]{7}}\right)$

15.

Use properties logarithms to condense the logarithmic expression as much as possible. Write the expression as a single logarithm whose coefficient is 1.

$\frac{1}{3}\ln\left(x\right)+\ln\left(y\right)-\ln\left(z\right)$

a)

$\ln\left(\frac{y\sqrt[3]{x}}{x}\right)$

b)

$\ln\left(\frac{x^3y}{z}\right)$

c)

$\ln\left(yz\sqrt[3]{x}\right)$

Logarithm Properties Take-Home Formative

Total questions: 15

Worksheet time: 39mins

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