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  1. s = 'TEStlabZ\nEDULABZ\nINTERNATIONAL\nLOGARITHMS AND INDICES\n\nQ.1. (A) Convert each of the following to logarithmic form.\n(i) \\( 5^{2}=25 \\)\n(ii) \\( 3^{-3}=\\frac{1}{27} \\)\n(iii) \\( (64)^{\\frac{1}{3}}=4 \\)\n(iv) \\( 6^{0}=1 \\)\n(v) \\( 10^{-2}=0.01 \\) (vi) \\( 4^{-1}=\\frac{1}{4} \\)\nAns. We know that \\( a^{b}=x \\Rightarrow b=\\log _{a} x \\)\n(i) \\( 5^{2}=25 \\quad \\therefore \\log _{5} 25=2 \\)\n(ii) \\( 3^{-3}=\\frac{1}{27} \\therefore \\log _{3}\\left(\\frac{1}{27}\\right)=-3 \\)\n(iii) \\( (64)^{\\frac{1}{3}}=4 \\therefore \\log _{64} 4=\\frac{1}{3} \\)\n(iv) \\( 6^{0}=1 \\quad \\therefore \\log _{6} 1=0 \\)\n(v) \\( 10^{-2}=0.01 \\therefore \\log _{10}(0.01)=-2 \\)\n(vi) \\( 4^{-1}=\\frac{1}{4} \\therefore \\log _{4}\\left(\\frac{1}{4}\\right)=-1 \\)\nQ.1. (B) Convert each of the following to exponential form.\n(i) \\( \\log _{3} 81=4 \\)\n(ii) \\( \\log _{8} 4=\\frac{2}{3} \\)\n(iii) \\( \\log _{2} \\frac{1}{8}=-3 \\)\n(iv) \\( \\log _{10}(0.01)=-2 \\)\n(v) \\( \\log _{5}\\left(\\frac{1}{5}\\right)=-1 \\) (vi) \\( \\log _{a} 1=0 \\)\nAns.\n(i) \\( \\log _{3} 81=4 \\quad \\therefore 3^{4}=81 \\)\n(ii) \\( \\log _{8} 4=\\frac{2}{3} \\quad \\therefore 8^{\\frac{2}{3}}=4 \\)\n(iii) \\( \\log _{2} \\frac{1}{8}=-3 \\quad \\therefore \\quad 2^{-3}=\\frac{1}{8} \\)\n(iv) \\( \\log _{10}(0.01)=-2 \\quad \\therefore \\quad 10^{-2}=0.01 \\)\n(v) \\( \\log _{5}\\left(\\frac{1}{5}\\right)=-1 \\quad \\therefore \\quad 5^{-1}=\\frac{1}{5} \\)\n(vi) \\( \\log _{a} 1=0 \\)\n\\( \\therefore a^{0}=1 \\)\nMath Class IX\n1\nQuestion Bank'
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TEStlabZ
EDULABZ
INTERNATIONAL
LOGARITHMS AND INDICES

Q.1. (A) Convert each of the following to logarithmic form.
(i) \( 5^{2}=25 \)
(ii) \( 3^{-3}=\frac{1}{27} \)
(iii) \( (64)^{\frac{1}{3}}=4 \)
(iv) \( 6^{0}=1 \)
(v) \( 10^{-2}=0.01 \) (vi) \( 4^{-1}=\frac{1}{4} \)
Ans. We know that \( a^{b}=x \Rightarrow b=\log _{a} x \)
(i) \( 5^{2}=25 \quad \therefore \log _{5} 25=2 \)
(ii) \( 3^{-3}=\frac{1}{27} \therefore \log _{3}\left(\frac{1}{27}\right)=-3 \)
(iii) \( (64)^{\frac{1}{3}}=4 \therefore \log _{64} 4=\frac{1}{3} \)
(iv) \( 6^{0}=1 \quad \therefore \log _{6} 1=0 \)
(v) \( 10^{-2}=0.01 \therefore \log _{10}(0.01)=-2 \)
(vi) \( 4^{-1}=\frac{1}{4} \therefore \log _{4}\left(\frac{1}{4}\right)=-1 \)
Q.1. (B) Convert each of the following to exponential form.
(i) \( \log _{3} 81=4 \)
(ii) \( \log _{8} 4=\frac{2}{3} \)
(iii) \( \log _{2} \frac{1}{8}=-3 \)
(iv) \( \log _{10}(0.01)=-2 \)
(v) \( \log _{5}\left(\frac{1}{5}\right)=-1 \) (vi) \( \log _{a} 1=0 \)
Ans.
(i) \( \log _{3} 81=4 \quad \therefore 3^{4}=81 \)
(ii) \( \log _{8} 4=\frac{2}{3} \quad \therefore 8^{\frac{2}{3}}=4 \)
(iii) \( \log _{2} \frac{1}{8}=-3 \quad \therefore \quad 2^{-3}=\frac{1}{8} \)
(iv) \( \log _{10}(0.01)=-2 \quad \therefore \quad 10^{-2}=0.01 \)
(v) \( \log _{5}\left(\frac{1}{5}\right)=-1 \quad \therefore \quad 5^{-1}=\frac{1}{5} \)
(vi) \( \log _{a} 1=0 \)
\( \therefore a^{0}=1 \)
Math Class IX
1
Question Bank
https://ideone.com/2iCK1c
language:
Python 3 (python  3.12)
created:
3 years ago
visibility:
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