Note: This is the Solution of exercise 2.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 2.2
Question # 01: Express each of the following in logarithmic form:
\((i)\) \(\quad\) \(10^3=1000 \)
\((ii)\) \(\quad\) \(2^8=256 \)
\((iii)\) \(\quad\) \(3^{-3}=\frac{1}{27}\)
\((iv)\) \(\quad\) \(20^2=400 \)
\((v)\) \(\quad\)\( 16^{-\frac{1}{4}}=\frac{1}{2} \)
\((vi)\) \( \quad\) \(11^2=121 \)
\((vii)\) \( \quad\) \(p=q^r \)
\((viii)\) \( \quad\) \((32)^{-\frac{1}{5}}=\frac{1}{2} \)
Question 2: Express each of the following in exponential form:
\((i)\) \(\quad\) \(log_5 125=3 \)
\((ii)\) \(\quad\) \(log_2 16=4\)
\((iii)\) \(\quad\) \(log_23 1=0 \)
\((iv)\) \(\quad \)\(log_5 5=1\)
\((v)\) \(\quad\) \(log_2 \frac{1}{8}=-3 \)
\((vi)\) \(\quad\) \(\frac{1}{2}=log_9 3 \)
\((vii)\) \(\quad\) \(5=log_{10} 100000 \)
\((viii)\) \(\quad\) \(log_4 \frac{1}{16} = -2 \)
Question 3: Find the value of \(x\) in each of the following:
\((i)\) \(\quad\) \(log_x 64=3 \)
\((ii)\) \(\quad\) \(log_5 1=x\)
\((iii)\) \(\quad\) \(log_x 8=1 \)
\((iv)\) \(\quad \)\(log_{10} x=-3\)
\((v)\) \(\quad\) \(log_4 x=\frac{3}{2} \)
\((vi)\) \(\quad\) \(log_2 1024=x \)