Note: This is the Solution of review exercise 2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Review Exercise 2
Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\) The standard form of \(5.2\times10^6\) is:
\( a) \quad \) \( 52,000 \)
\( b) \quad \) \( 520,000\)
\(c) \quad \) \( 5,200,000\)
\( d) \quad \) \( 52,000,000\)
\( \text{Answer/Explanation}\)
\((ii)\) Scientific notation of \(0.00034\) is:
\( a) \quad \) \( 3.4\times 10^3\)
\( b) \quad \) \( 3.4\times 10^{-4}\)
\(c) \quad \) \(3.4\times 10^4 \)
\( d) \quad \) \(3.4\times 10^{-3} \)
\( \text{Answer/Explanation}\)
\((iii)\) The base of common logarithm is:
\( a) \quad \) \( 2\)
\( b) \quad \) \(10 \)
\(c) \quad \) \(5 \)
\( d) \quad \) \( e\)
\( \text{Answer/Explanation}\)
\((iv)\)\(\quad\)\(log_2\ 2^3=\_\_\_\_\_.\)
\( a) \quad \) \(1 \)
\( b) \quad \) \( 2\)
\(c) \quad \) \( 5\)
\( d) \quad \) \( 3\)
\( \text{Answer/Explanation}\)
\((v)\) \(\quad\) \(log\ 100=\_\_\_\_\_.\)
\( a) \quad \) \(2 \)
\( b) \quad \) \(3 \)
\(c) \quad \) \( 10\)
\( d) \quad \) \( 1\)
\( \text{Answer/Explanation}\)
\((vi)\) If \(log\ 2=0.3010\), then \(log\ 200\) is:
\( a) \quad \) \( 1.3010\)
\( b) \quad \) \( 0.6010\)
\(c) \quad \) \( 2.3010\)
\( d) \quad \) \( 2.6010\)
\( \text{Answer/Explanation}\)
\((vii)\)\(\quad\)\( log(0)=\_\_\_\_.\)
\( a) \quad \) positive
\( b) \quad \) negative
\(c) \quad \) zero
\( d) \quad \) undefined
\( \text{Answer/Explanation}\)
\((viii)\)\(\quad\) \(log\ 10,000=\_\_\_\_.\)
\( a) \quad \) \( 2\)
\( b) \quad \) \( 3\)
\(c) \quad \) \( 4\)
\( d) \quad \) \( 5\)
\( \text{Answer/Explanation}\)
\((ix)\)\(\quad\)\(log\ 5+log\ 3=\_\_\_\_.\)
\( a) \quad \) \(log\ 0\)
\( b) \quad \) \(log\ 2\)
\(c) \quad \) \(log\left(\frac{5}{3}\right)\)
\( d) \quad \) \(log\ 15\)
\( \text{Answer/Explanation}\)
\((x)\) \(\quad\) \(3^4=81\) in logarithmic form is:
\( a) \quad \) \( log_3\ 4=81\)
\( b) \quad \) \(log_4\ 3=81 \)
\(c) \quad \) \(log_3\ 81=4 \)
\( d) \quad \) \( log_4\ 81=3\)
\( \text{Answer/Explanation}\)
Question 2: Express the following numbers in sceintific notation:
\((i)\) \(\quad\) \(0.000567 \)
\((ii)\) \(\quad\) \(734 \)
\((iii)\) \(\quad\) \(0.33\times 10^3 \)
Question 3: Express the following numbers in ordinary notation.
\((i)\) \(\quad\) \(2.6\times 10^3 \)
\((ii)\) \(\quad\) \(8.794\times 10^{-4} \)
\((iii)\) \(\quad\) \(6\times 10^{-6} \)
Question 4: Express each of the following in logarithmic form:
\((i)\) \(\quad\) \(3^7=2187 \)
\((ii)\) \(\quad\) \(a^b=c \)
\((iii)\) \(\quad\) \((12)^2=144 \)
Question 5: Express each of the following in exponential form:
\((i)\) \(\quad\) \(log_4\ 8=x \)
\((ii)\) \(\quad\) \(log_9\ 729=3 \)
\((iii)\) \(\quad\) \(log_4\ 1024=5 \)
Question 6: Find value of \(x\) in the following:
\((i)\) \(\quad\) \(log_{9} \ x=0.5 \)
\((ii)\) \(\quad\) \(\left(\frac{1}{9}\right)^{3x} =27 \)
\((iii)\) \(\quad\) \(\left(\frac{1}{32}\right)^{2x} =64 \)
Question 7: Write the following as a single logartihm:
\((i)\) \(\quad\) \(7\ log\ x-3\ log\ y^{2}\)
\((ii)\) \(\quad\) \(3\ log\ 4-log\ 32 \)
\((iii)\) \(\quad\) \(\frac{1}{3}( log_{5} \ 8+log_{5} \ 27) -log_{5} \ 3\)
Question 8: Expand the following using laws of logarithms:
\((i)\) \(\quad\) \(log\left( x\ y\ z^{6}\right)\)
\((ii)\) \(\quad\) \(log_{3} \ \sqrt[6]{m^{5} n^{3}} \)
\((iii)\) \(\quad\) \(log\sqrt{8x^{3}}\)
Question 9: Find the values of the following with the help of logarithm table:
\((i)\) \(\quad\) \(\sqrt[3]{68.24}\)
\((ii)\) \(\quad\) \(319.8\times 3.543\)
\((iii)\) \(\quad\) \(\large{\frac{36.12\times 750.9}{113.2\times 9.98}}\)