Free Printable Revision Chapter 4 : Indices, Surds and Logarithms

1.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

2.

m² × n³ × m⁶ =

a)

m⁸n³

b)

m⁶n³

c)

mn¹¹

d)

mnm¹¹

3.

(3x²y³)²

a)

9x⁴y⁶

b)

3x⁴y⁵

c)

6x⁴y⁶

d)

9xy

4.

Simplify

a)

A

b)

B

c)

C

d)

D

5.

Simplify $\frac{3^n\times9^{n+1}}{3^{n-1}\times9^{n-1}}$ .

a)

3

b)

27

c)

81

d)

243

6.

Find the value of x if 16^{2x − 1}= 64.

a)

1.5

b)

1.25

c)

−1.25

d)

$\frac{4}{5}$

7.

Simplify the following surd...

a)

2√2

b)

4√2

c)

2√4

d)

3√2

8.

Rationalise the Denominator:
³/_√5

a)

³^√5/₅

b)

³^√5/₂₅

c)

^√5/₅

d)

^√5/3

9.

Simplify completely:
2√3 + 4√3

a)

6√3

b)

6√6

c)

8√3

d)

8√6

10.

a)

$6+\sqrt{7}$

b)

$\frac{3+\sqrt{7}}{5}$

c)

$\sqrt{5}+12$

d)

$6+\sqrt{35}$

11.

Write 5² = 25 in logarithm form.

a)

log₅2 = 25

b)

log₂₅5 = 2

c)

log₂25 = 5

d)

log₅25 = 2

12.

Write $2^{-4}=\frac{1}{16}$ in logarithm form.

a)

$\log_2\left(\frac{1}{16}\right)=-4$

b)

$\log_{-4}2=\frac{1}{16}$

c)

$\log_{-4}\left(\frac{1}{16}\right)=2$

d)

$\log_{2x}\left(-4\right)=\frac{1}{16}$

13.

Express $\log_232=5$ in index form.

a)

$2^{-5}=32$

b)

$2^5=32$

c)

$2^{32}=5$

d)

$32^5=2$

14.

Express $\log_2\left(\frac{1}{8}\right)=-3$ in index form.

a)

$2^{-3}=\frac{1}{8}$

b)

$-3^2=\frac{1}{8}$

c)

$2^{\frac{1}{8}}=-3$

d)

$-3^{\frac{1}{8}}=2$

15.

Evaluate log₃81.

a)

$4$

b)

$-4$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

16.

Evaluate 3 log₂4.

a)

3

b)

2

c)

6

d)

4

17.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

18.

Simplify log₃9 + log₃27.

a)

−1

b)

4

c)

5

d)

1

19.

Given log₅(4x − 7) = log₅(x + 5).

Find the value of x.

a)

3

b)

4

c)

7

d)

12

20.

Solve for x

a)

x = 8

b)

x = 4

c)

x = 256

d)

x = 32

Revision Chapter 4 : Indices, Surds and Logarithms

Total questions: 20

Worksheet time: 54mins

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