Free Printable Logarithm (Concluding part)

1.

Condense to a single logarithm.

a)

ln x⁴/ y

b)

ln xy⁴

c)

ln x/ y⁴

d)

ln x⁴/ y⁴

2.

Solve:
log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

3.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

4.

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)

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

5.

Expand the following: $\log\left(j^4k^7\right)$

a)

$\log\left(4j\right)+\log\left(7k\right)$

b)

$11\log\left(j+k\right)$

c)

$28\log\left(jk\right)$

d)

$4\log\left(j\right)+7\log\left(k\right)$

6.

Use Logarithm table to evaluate $\frac{\sqrt[3]{0.5915}}{17.8^2}$ (2005 NEC0)

a)

$2.64938\ \times10^{-3}$

b)

0.00265

c)

0.00089

d)

0.00234

7.

Evaluate using logarithm tables. $\frac{3.87^{3\ }+20}{3.87^3\ -20}$

a)

2.054

b)

2.05

c)

2.0

d)

2

8.

Evaluate using Logarithm tables : $\frac{1.487^3\ -\ 1}{1.487^3\ +\ 1}$

a)

0.5338

b)

0.534

c)

0.532

d)

0.678

9.

Express the square root of 0.000144 in standard form.

a)

$1.2\ \times\ 10^{-4}$

b)

$1.2\ \times\ 10^{-3}$

c)

$1.2\ \times\ 10^{-2}$

d)

$1.2\ \times\ 10^{-6}$

10.

Which of these statements about $y=8\ \sqrt[]{m}\ \ is\ correct\ ?$

a)

$\log\ y=\log8\times\log\ \sqrt[]{m}$

b)

$\log\ y=3\log2\ \times\ \frac{1}{2}\log\ m$

c)

$\log\ y=3\log2\ -\ \frac{1}{2}\log\ m$

d)

$\log\ y=\ 3\log2\ +\ \frac{1}{2}\log\ m$

11.

Solve the logarithmic equation : log₅ $\left(x^2-9\right)=0$

a)

5

b)

-5

c)

0

d)

√10, -√10

12.

Solve the equations : $\log\left(x^2+6x\right)=1.4314$

Note: The question should be changed to indices as x² + 6x = 10^1.4314

The value of 10^1.4314 is same as the antilog of 1.4314.

a)

9 or -3

b)

-9 or 5

c)

-9 or 3

d)

5 or 9

13.

If log₁₀ $x=\overline{2}.7087,\ find\ x$

a)

0.01866

b)

0.02913

c)

0.05113

d)

128.0

14.

Given that $\frac{2x\ -y}{2y-x}=6,\ find\ the\ ratio\ x:y$

a)

13:8

b)

15:10

c)

10:5

d)

12:7

15.

Evaluate 10^2.6457

Note: This is the same as finding the antilog of 2.6457

a)

400.1

b)

512.3

c)

442.3

d)

350.5

16.

In changing the base of the logarithm log_ef, which of these is correct?

a)

log_fe

b)

$\frac{\log_fe}{1}$

c)

Both b and d

d)

$\frac{1}{\log_fe}$

17.

What is the value of log_aa⁴ ?

a)

1

b)

2

c)

4

d)

a

18.

Given that $\log_a2=0.693\ and\ \log_a3=1.097,\ find\ \log_a13.5.$

a)

1.404

b)

1.790

c)

2.598

d)

2.790

19.

Evaluate using logarithm tables : $\left(\sqrt[5]{\frac{26.7}{9562}}\right)$

a)

0.4561

b)

0.3084

c)

0.582

d)

0.215

20.

Simplify this logarithm with bar notation : $\overline{3}.8\ \div\ 4$

a)

0.75

b)

$\overline{2}.2$

c)

$\overline{1}.45$

d)

$\overline{0}.95$

Logarithm (Concluding part)

Total questions: 20

Worksheet time: 56mins

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