{(0.05)^{{{log }_{_{√ {20} }}}(0.1 + 0.01 + 0.001 + ......)}}= . . . .

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Basic of Logarithms

hard

${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}= . .$ . .

$81$

${1 \over {81}}$

$20$

$0.05$

Solution

(a) ${(0.05)^{{{\log }_{\sqrt {20} }}(0.1 + 0.01 + ……)}} = {\left( {{1 \over {20}}} \right)^{2{{\log }_{20}}\left( {{{0.1} \over {1 – 0.1}}} \right)}}$

$ = {20^{ – 2{{\log }_{20}}(1/9)}} = {20^{2{{\log }_{20}}9}} = {20^{{{\log }_{20}}{9^2}}} = {9^2} = 81$.

Standard 11

Mathematics

$\sqrt {(\log _{0.5}^24)} = . . $. .

easy

જો $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$ તો $xyz = . . . .$

easy

${\log _2}7$ એ . . . . થાય.

easy

(IIT-1990)

જો ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| – 3}}{{\left| z \right| + 1}}} \right)\, < \, – 2$ હોય તો

normal

જો ${\log _{1/\sqrt 2 }}\sin x > 0,x \in [0,\,\,4\pi ],$ તો $ x$ ની કેટલી કિમતો મળે કે જે ${\pi \over 4}$ નો ગુણિત છે.

hard

${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}= . .$ . .

Solution

Similar Questions

$\sqrt {(\log _{0.5}^24)} = . . $. .

જો $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$ તો $xyz = . . . .$

${\log _2}7$ એ . . . . થાય.

જો ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| – 3}}{{\left| z \right| + 1}}} \right)\, < \, – 2$ હોય તો

જો ${\log _{1/\sqrt 2 }}\sin x > 0,x \in [0,\,\,4\pi ],$ તો $ x$ ની કેટલી કિમતો મળે કે જે ${\pi \over 4}$ નો ગુણિત છે.

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