Quiz about Logarithm (Concluding part)

Question 1

Condense to a single logarithm.

Accepted Answer

ln x/ y4

Answer

ln x4/ y

Answer

ln xy4

Answer

ln x⁴/ y⁴

Question 2

Solve:
log₉(x)+log₉(x+2)=log₉(35)

Accepted Answer

5

Answer

-7

Answer

5, -7

Answer

-7, -13

Question 3

log₅(4x-7)=log₅(x+5)

Accepted Answer

4

Answer

3

Answer

12

Answer

7

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

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

Accepted Answer

0.00265

Answer

$$2.64938\ imes10^{-3}$$

Answer

0.00089

Answer

0.00234

Question 7

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

Accepted Answer

2.054

Answer

2.05

Answer

2.0

Answer

2

Question 8

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

Accepted Answer

0.5338

Answer

0.534

Answer

0.532

Answer

0.678

Question 9

Express the square root of 0.000144 in standard form.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 10

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

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.

Accepted Answer

-9 or 3

Answer

9 or -3

Answer

-9 or 5

Answer

5 or 9

Question 12

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

Accepted Answer

0.05113

Answer

0.01866

Answer

0.02913

Answer

128.0

Question 13

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

Accepted Answer

13:8

Answer

15:10

Answer

10:5

Answer

12:7

Question 14

Evaluate 10^2.6457

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

Accepted Answer

442.3

Answer

400.1

Answer

512.3

Answer

350.5

Question 15

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

Accepted Answer

$$\frac{1}{\log_fe}$$

Answer

logfe

Answer

$$\frac{\log_fe}{1}$$

Answer

Both b and d

Question 16

What is the value of log_aa⁴ ?

Accepted Answer

4

Answer

1

Answer

2

Answer

a

Question 17

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

Accepted Answer

2.598

Answer

1.404

Answer

1.790

Answer

2.790

Question 18

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

Accepted Answer

0.3084

Answer

0.4561

Answer

0.582

Answer

0.215

Question 19

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

Accepted Answer

$$\overline{1}.45$$

Answer

0.75

Answer

$$\overline{2}.2$$

Answer

$$\overline{0}.95$$

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