Math 9th Chap 2 : Topic 4 - Maryam Publications

Math Chapter 2 : Topic 4

Log Laws and Applications

1 / 20

Which logarithmic law is correctly used to convert exponential growth $N = N_{0}\ a^{t}$ into a linear form?

A) $log(a - b) = log\ a - log\ b$

B) $log(a^{t}) = t\ log\ a$

C) $\log(ab) = log\ a\ .\ \ log\ b$

D) $log(a + b) = log\ a + log\ b$

2 / 20

In population growth, if $N = N_{0\ }e^{kt}$, taking natural log helps to:

A) Linearize the equation in terms of time

B) Change base of exponent only

C) Remove constants

D) Eliminate multiplication

3 / 20

If a quantity decreases exponentially, which law helps to find time $(t)$?

A) Quotient law of logs

B) Power law of logs

C) Change of base only

D) Product law of logs

4 / 20

Sound intensity level is given by $L = 10\ \log_{10}\ ({I\ /\ I}_{0})$. If intensity increases $100$ times, the increase in decibel level is:

A) $2\ dB$

B) $10\ dB$

C) $100\ dB$

D) $20\ dB$

5 / 20

If sound intensity doubles, the increase in decibel level is approximately:

A) $1\ dB$

B) $10\ dB$

C) $3\ dB$

D) $2\ dB$

6 / 20

Which situation represents exponential decay?

A) Population increase

B) Bank interest growth

C) Radioactive substance reduction

D) Compound interest

7 / 20

Which law explains $log(ab) = log\ a + log\ b$ in real-life growth models?

A) Product law

B) Change of base

C) Quotient law

D) Power law

8 / 20

If a population becomes $3$ times larger, the log expression changes as:

A) $log\ 3N = log\ N\ 3$

B) $log\ 3N = 3log\ N$

C) $log\ 3N = log\ 3 + log\ N$

D) $log\ 3N = log\ N - log\ 3$

9 / 20

In decay problems, taking logarithm is useful because it:

A) Removes time variable

B) Converts multiplication into addition

C) Eliminates constants completely

D) Converts exponential into linear form

10 / 20

If sound intensity ratio is $I_{2}\ /\ I_{1} = 1000$, decibel difference is:

A) $3\ dB$

B) $100\ dB$

C) $30\ dB$

D) $10\ dB$

11 / 20

Which law is used when solving $log\ (a^{b})$ in growth models?

A) $log\ a\ \ .\ \ log\ b$

B) $b\ log\ a$

C) $log\ a + log\ b$

D) $log\ a - log\ b$

12 / 20

If decibel level increases from $40\ dB$ to $60\ dB$, intensity increases by:

A) $2$ times

B) $100$ times

C) $10$ times

D) $20$ times

13 / 20

Which of the following best describes use of logarithms in real life?

A) Converting addition into multiplication

B) Making numbers larger

C) Simplifying exponential relationships

D) Removing constants from equations

14 / 20

A radioactive substance halves every hour. Which mathematical form best represents it?

A) Constant function

B) Exponential decay form

C) Linear form

D) Quadratic form

15 / 20

Why are logarithms used in sound measurement?

A) To avoid negative numbers

B) To compress large intensity values

C) To remove noise

D) To increase sound

16 / 20

If $L = 10\ log\ (I\ /\ I_{0})$, then doubling intensity results in:

A) No change

B) Decrease in level

C) Small increase $(\sim 3\ dB)$

D) Addition of $10\ dB$

17 / 20

Which transformation is used to solve for time in exponential growth?

A) Taking square root

B) Taking logarithm

C) Differentiation

D) Integration

18 / 20

If two sounds differ by $10\ dB$, the intensity ratio is:

A) $2$ times

B) $100$ times

C) $1$ time

D) $10$ times

19 / 20

Which law is applied when separating log of a quotient in decay analysis?

A) $log\ (a/b) = log\ a + log\ b$

B) $log\ (a/b) = log\ a - log\ b$

C) $log\ (a/b) = b\ log\ a$

D) $log\ (a/b) = log\ a\ \ .\ \ log\ b$

20 / 20

In real-life modeling, logarithms are mainly used to:

A) Replace all algebraic operations

B) Handle exponential changes efficiently

C) Solve trigonometric equations

D) Make graphs nonlinear

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