Free Printable Indices and Logarithms

1.

Find $b^{10}\div b^2$

a)

$b^5$

b)

$b^{12}$

c)

$b^8$

d)

$b^{20}$

2.

$\frac{y^5}{y^{-3}\times y^2}$

a)

$y^4$

b)

$y^6$

c)

$y^5$

d)

$6y$

3.

If $5^n=125$ , find n.

a)

25

b)

$\frac{1}{3}$

c)

-3

d)

3

4.

Evaluate the following logarithm $\log_33$

a)

1

b)

-1

c)

0

d)

$\frac{1}{2}$

5.

Write in exponential form $\log_28=3$

a)

$2^3=8$

b)

$3^2=8$

c)

$2^8=3$

d)

$3^8=2$

6.

Evaluate $\log_{\frac{1}{2}}1$

a)

2

b)

1

c)

$\frac{1}{2}$

d)

0

7.

Solve $3^{3x+6}=\frac{1}{27}$

a)

$x=-1$

b)

$x=-9$

c)

$x=6$

d)

$x=-3$

8.

Simplify $\frac{1}{2}\log_{ }4-\log_{ }6$

a)

$\log_{ }3$

b)

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

c)

$\log_{ }\left(\frac{2}{3}\right)$

d)

$\log_{ }\left(\frac{1}{3}\right)$

9.

Simplify log₃9 + log₃27.

a)

-1

b)

4

c)

5

d)

1

10.

Write $2^{-4}=\frac{1}{16}$ in logarithmic equat

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)

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

Indices and Logarithms

Total questions: 10

Worksheet time: 5mins

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