Free Printable revision CHAPTER 1

1.

Choose the correct rules of indices

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m+a^n=a^{mn}$

c)

$\left(a^m\right)^n=a^{mn}$

d)

$\frac{a^m}{a^n}=a^{m-n}$

e)

$a^m-a^n=a^{\frac{m}{n}}$

2.

Write $5x\times5x\times5x\times5x\$ in exponent form

a)

$5x^4$

b)

$\left(5x\right)^4$

c)

$625x$

d)

$none$

3.

Simplify

a)

A

b)

B

c)

C

d)

D

4.

Solve $4^{a-1}=8^{a+3}$ .

a)

$a=-11$

b)

$a=-4$

c)

$a=4$

d)

$a=11$

5.

Solve $3^{a+3}-3^{a+2}=2\ \ \$ .

a)

$a=-2$

b)

$a=\frac{1}{2}$

c)

$a=2$

d)

No solution

6.

Solve $4^{2x-1}=64^x$ .

a)

$x=1$

b)

$x=-1$

c)

$x=-\frac{1}{4}$

d)

$x=\frac{1}{4}$

7.

Solve

\sqrt{x+1}=3-\sqrt{x}

a)

$\frac{4}{3}$

b)

2

c)

3

d)

$\frac{16}{9}$

8.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

9.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

a)

log₅7

b)

log₅12

c)

log₇5

d)

3log₅4

10.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

11.

Select the true equation

a)

$9^{-2}=-81$

b)

$9^{-2}=\frac{1}{18}$

c)

$9^{-2}=\frac{1}{81}$

d)

$9^{-2}=-18$

e)

$9^{-2}=3$

12.

If $\log_3x=-2$ , then the value of $x$ is

a)

$-6$

b)

$-\frac{3}{2}$

c)

$\frac{2}{3}$

d)

$\frac{1}{6}$

e)

$\frac{1}{9}$

13.

Evaluate the following logarithm:

log₆36

a)

3

b)

2

c)

1

d)

0

14.

Simplify the following: $\log_5\left(3\right)+\log_5\left(r\right)-\log_5\left(w\right)$

a)

$\log_5\left(3rw\right)$

b)

$\log_5\left(3+r-w\right)$

c)

$\log_5\left(\frac{3r}{w}\right)$

d)

$\frac{\log_5\left(3r\right)}{\log_5\left(w\right)}$

15.

Which is an equivalent statement to $y=2^x$ ?

a)

$x=2^y$

b)

$\log_xy=2$

c)

$\log_2x=y$

d)

$\log_2y=x$

16.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

17.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

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

d)

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

18.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(8x\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

$\log_98x$

19.

Expand the logarithm.
$\log_4\sqrt{x^3y}$

a)

$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

b)

$\frac{3}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

c)

$\frac{1}{2}\log_4\left(x\right)-\log_4\left(y\right)$

d)

$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$

20.

Expand . $\log_6\left(\frac{5x^3}{y}\right)$

a)

$\log_65x^3-\log_6y$

b)

$\log_65+\log_6x^3-\log_6y$

c)

$\log_65+3\log_6x-\log_6y$

d)

$\log_65+3\log_6x+\log_6y$

revision CHAPTER 1

Total questions: 20

Worksheet time: 5mins

Similar Resources on Wayground