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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