Free Printable HNPC Unit 4 Exp and Log Quiz

1.

Convert the equation

4^{-2}=\frac{1}{16}

to logarithmic form.

a)

b)

c)

d)

e)

2.

Solve for x:

a)

$-\frac{13}{3}$

b)

$-\frac{3}{5}$

c)

$\frac{7}{5}$

d)

$-\frac{7}{3}$

3.

Write the expression

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

as a single logarithm.

a)

b)

c)

d)

e)

4.

Evaluate

a)

$\frac{1}{3}$

b)

3

c)

d)

$e$

e)

can't be evaluated

5.

Evaluate:

\log_464

a)

$\frac{1}{3}$

b)

2

c)

4

d)

3

e)

16

6.

Simplify:

\left(-2x^3\right)^4

a)

$-16x^{12}$

b)

$16x^{12}$

c)

$-16x^7$

d)

$-8x^{12}$

e)

$16x^7$

7.

Solve for x:

8=\log\left(x+1\right)

a)

100,000

b)

99,999,999

c)

100,000,001

d)

10,000,000

8.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

9.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

10.

Without a calculator, determine which of the following ISN'T possible. CHECK ALL THAT APPLY.

a)

log₂ (x - 4) when x = 4

b)

log₃ (x+3) when x = 0

c)

-2log₅ (x-1) when x = 0

d)

¹/₂log (x+4) when x = -2

11.

Expand: $\log_9\sqrt{23}$

a)

$\frac{1}{2}\log_923$

b)

$\log_9\left(\frac{1}{2}\right)-\log_923$

c)

$\log_9\sqrt{2}+\log_9\sqrt{3}$

d)

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

12.

Use the properties of logarithms to fully expand the expression. Write powers as factors.

\log_a\ \frac{4y\sqrt{3x+2}}{\left(x-5\right)^4}

a)

$\log_a4+\log_ay-\log_a\left(3x+2\right)+4\log_a\left(x-5\right)$

b)

$\log_a4y+\log_a\sqrt{3x+2}-4\log_a\left(x-5\right)$

c)

$\log_a4+\log_ay+\frac{1}{2}\log_a\left(3x+2\right)-4\log_a\left(x-5\right)$

d)

$\log_a4y+\frac{1}{2}\log_a\left(3x+2\right)-\log_a\left(x-5\right)^4$

e)

$\log_a4-\log_ay-\log_a\ \frac{1}{2}+\log_a\left(3x+2\right)+4\log_a\left(x-5\right)$

13.

In the logarithmic equation

\log_ax=y

,the value of y can be any real number.

a)

True

b)

False

14.

Use the properties of logarithms to condense the expression. Write the expression as a single logarithm with all factors written as exponents.

\log x-2\log y+3\log z

a)

$\log\ \frac{z^3}{xy^2}$

b)

$\log\ \frac{x\times3z}{2y^{ }}$

c)

$\log\ \frac{x}{y^2z^3}$

d)

$\log\ \frac{xz^3}{y^2}$

HNPC Unit 4 Exp and Log Quiz

Total questions: 14

Worksheet time: 40mins

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